Existence of periodic orbits of autonomous retarded functional differential equations

DOI10.1017/S0305004100057376zbMath0435.34062OpenAlexW2112152629MaRDI QIDQ3874571

Russell A. Smith

Publication date: 1980

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0305004100057376

zbMATH Keywords

omega limit setretarded functional differential equationsPoincare-Bendixson theoremvector control equations with retarded feedbacks

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Functional-differential equations (including equations with delayed, advanced or state-dependent argument) (34K99)

Related Items (5)

Existence, Uniqueness, and Stability of Slowly Oscillating Periodic Solutions for Delay Differential Equations with Nonnegativity Constraints ⋮ Frequency theorem and inertial manifolds for neutral delay equations ⋮ Non-trivial periodic solutions for a class of second order differential equations with large delay ⋮ A Poincaré-Bendixson theorem for scalar reaction diffusion equations ⋮ Discrete Ljapunov functionals and $\omega $-limit sets

Cites Work

• The existence of periodic solutions of \(f'(x)=-\alpha f(x-1)(1+f(x))\)
• Periodic solutions of some nonlinear autonomous functional differential equations
• Theory of functional differential equations. 2nd ed
• Integral averaging and bifurcation
• Periodic solutions of autonomous equations
• Differential equations: Stability, oscillations, time lags
• A periodicity theorem for autonomous functional differential equations
• A bifurcation problem for a functional differential equation of finitely retarded type
• The Poincaré–Bendixson theorem for certain differential equations of higher order
• Functional differential equations
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