34Kxx Functional-differential equations
This subtopic studies functional differential equations, where delays or functional dependence make the dynamics depend on past or distributed states.
Specific topics
34K05 General theory of functional-differential equations
Overview
34K05 studies general theory of functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for general theory of functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K06 Linear functional-differential equations
Overview
34K06 studies linear functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for linear functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K07 Theoretical approximation of solutions to functional-differential equations
Overview
34K07 studies theoretical approximation of solutions to functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for theoretical approximation of solutions to functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K08 Spectral theory of functional-differential equations
Overview
34K08 studies spectral theory of functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for spectral theory of functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K09 Functional-differential inclusions
Overview
34K09 studies functional-differential inclusions in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for functional-differential inclusions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K10 Boundary value problems for functional-differential equations
Overview
34K10 studies boundary value problems for functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for boundary value problems for functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K11 Oscillation theory of functional-differential equations
Overview
34K11 studies oscillation theory of functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for oscillation theory of functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K12 Growth, boundedness, comparison of solutions to functional-differential equations
Overview
34K12 studies growth, boundedness, comparison of solutions to functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for growth, boundedness, comparison of solutions to functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K13 Periodic solutions to functional-differential equations
Overview
34K13 studies periodic solutions to functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for periodic solutions to functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K14 Almost periodic solutions to functional-differential equations
Overview
34K14 studies almost periodic solutions to functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for almost periodic solutions to functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K17 Transformation and reduction of functional-differential equations
Overview
34K17 studies transformation and reduction of functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for transformation and reduction of functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K18 Bifurcation theory of functional-differential equations
Overview
34K18 studies bifurcation theory of functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for bifurcation theory of functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K19 Invariant manifolds of functional-differential equations
Overview
34K19 studies invariant manifolds of functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for invariant manifolds of functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K20 Stability theory of functional-differential equations
Overview
34K20 studies stability theory of functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for stability theory of functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K21 Stationary solutions of functional-differential equations
Overview
34K21 studies stationary solutions of functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for stationary solutions of functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K23 Complex (chaotic) behavior of solutions to functional-differential equations
Overview
34K23 studies complex (chaotic) behavior of solutions to functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for complex (chaotic) behavior of solutions to functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K25 Asymptotic theory of functional-differential equations
Overview
34K25 studies asymptotic theory of functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for asymptotic theory of functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K26 Singular perturbations for functional-differential equations
Overview
34K26 studies singular perturbations for functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for singular perturbations for functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K28 Numerical approximation of solutions to functional-differential equations
Overview
34K28 studies numerical approximation of solutions to functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for numerical approximation of solutions to functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K29 Inverse problems for functional-differential equations
Overview
34K29 studies inverse problems for functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for inverse problems for functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K30 Functional-differential equations in abstract spaces
Overview
34K30 studies functional-differential equations in abstract spaces in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for functional-differential equations in abstract spaces
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K31 Lattice functional-differential equations
Overview
34K31 studies lattice functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for lattice functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K32 Implicit functional-differential equations
Overview
34K32 studies implicit functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for implicit functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K33 Averaging for functional-differential equations
Overview
34K33 studies averaging for functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for averaging for functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K34 Hybrid functional-differential equations
Overview
34K34 studies hybrid functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for hybrid functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K35 Control problems involving functional-differential equations
Overview
34K35 studies control problems involving functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for control problems involving functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K36 Fuzzy functional-differential equations
Overview
34K36 studies fuzzy functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for fuzzy functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K37 Functional-differential equations with fractional derivatives
Overview
34K37 studies functional-differential equations with fractional derivatives in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for functional-differential equations with fractional derivatives
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K38 Functional-differential inequalities
Overview
34K38 studies functional-differential inequalities in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for functional-differential inequalities
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K40 Neutral functional-differential equations
Overview
34K40 studies neutral functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for neutral functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K45 Functional-differential equations with impulses
Overview
34K45 studies functional-differential equations with impulses in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for functional-differential equations with impulses
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K50 Stochastic functional-differential equations
Overview
34K50 studies stochastic functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for stochastic functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks
34K60 Qualitative investigation and simulation of models involving functional-differential equations
Overview
34K60 studies qualitative investigation and simulation of models involving functional-differential equations in functional differential equations. It studies equations where the derivative depends on delayed or advanced values of the unknown function.
Related Wikipedia Page
Functional Differential Equations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for qualitative investigation and simulation of models involving functional-differential equations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in population dynamics, control, and systems with memory.
Applications
- Delay and neutral equations
- Systems with memory
- Biological and control models
References
Recommended Textbooks