Nontrivial periodic solutions for delay differential systems via Morse theory

DOI10.1016/j.na.2010.11.003zbMath1223.34099OpenAlexW2059552861MaRDI QIDQ629311

Qiong Meng, Xiaosheng Zhang

Publication date: 9 March 2011

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.11.003

zbMATH Keywords

Galerkin methodMorse theorydelay systemsSymmetric periodic solutionsvarational structure

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Periodic solutions to functional-differential equations (34K13)

Related Items

Periodic solutions for a class of second order delay differential systems ⋮ The existence of periodic solutions for second-order delay differential systems ⋮ Periodic solutions of delay differential systems via Hamiltonian systems ⋮ Periodic solutions of second-order differential equations with multiple delays ⋮ Nontrivial periodic solutions to delay difference equations via Morse theory ⋮ NONTRIVIAL PERIODIC SOLUTIONS FOR SECOND-ORDER DIFFERENTIAL DELAY EQUATIONS ⋮ Retracted Article: Landesman-Lazer type condition for second-order differential equations at resonance with impulsive effects ⋮ Multiple periodic solutions to a class of nonautonomous second-order delay differential equation ⋮ Infinitely many periodic solutions to delay differential equations via critical point theory ⋮ Periodic solutions for nonautonomous first order delay differential systems via Hamiltonian systems ⋮ Unnamed Item ⋮ Existence theorems for some abstract nonlinear non-autonomous systems with delays

Cites Work

• The existence of periodic solutions of \(f'(x)=-\alpha f(x-1)(1+f(x))\)
• Circulant matrices and differential-delay equations
• Critical point theory and Hamiltonian systems
• Ordinary differential equations which yield periodic solutions of differential delay equations
• On the nonlinear differential delay equation x'(t) = -f(x(t),x(t-1))
• Nontrivial periodic solutions for the asymptotically linear Hamiltonian systems with resonance at infinity
• Introduction to functional differential equations
• Periodic solutions for functional differential equations with multiple state-dependent time lags
• Infinite dimensional Morse theory and multiple solution problems
• Bifurcations of periodic solutions of delay differential equations
• Solutions of \(\dot x(t)=-g(x(t-1))\) approach the Kaplan-Yorke orbits for odd sigmoid \(g\)
• Delay equations. Functional-, complex-, and nonlinear analysis
• The Poincaré-Bendixson theorem for monotone cyclic feedback systems with delay
• A further generalization of the Schauder fixed point theorem
• Periodic solutions of nonlinear functional differential equations
• Multiplicity results for periodic solutions to delay differential equations via critical point theory
• Characteristic Multipliers and Stability of Symmetric Periodic Solutions of . x   (t) = g(x(t - 1))
• Existence of periodic solutions of two-dimensional differential-delay equations
• A Hopf Global Bifurcation Theorem for Retarded Functional Differential Equations
• On Critical Point Theory for Indefinite Functionals in The Presence of Symmetries
• Periodic solutions of some differential delay equations created by Hamiltonian systems
• Critical point theory for asymptotically quadratic functionals and applications to problems with resonance
• Applications of a \(Z_p\) index theory to periodic solutions for a class of functional-differential equations
• Unnamed Item

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