The existence of periodic solutions of delay differential equations by \(E^+\)-Conley index theory

DOI10.1155/2022/3396716zbMath1504.34195OpenAlexW4224262087MaRDI QIDQ2672492

Huafeng Xiao

Publication date: 10 June 2022

Published in: Journal of Function Spaces (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2022/3396716

zbMATH Keywords

periodic solutionsConley indexdelay differential systems

Mathematics Subject Classification ID

Periodic solutions to functional-differential equations (34K13) Index theory for dynamical systems, Morse-Conley indices (37B30)

Cites Work

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• Periodic solutions of asymptotically linear delay differential systems via Hamiltonian systems
• Multiplicity results of periodic solutions for a class of second order delay differential systems
• Multiplicity results on periodic solutions to higher-dimensional differential equations with multiple delays
• Multiplicity results on period solutions to higher dimensional differential equations with multiple delays
• The existence of periodic solutions of \(f'(x)=-\alpha f(x-1)(1+f(x))\)
• Existence of multiple periodic solutions for a class of second-order delay differential equations
• 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))
• Periodic solutions of some nonlinear, autonomous functional differential equations. II
• Periodic solutions of some nonlinear autonomous functional differential equations
• The Fuller index and global Hopf bifurcation
• A new cohomology for the Morse theory of strongly indefinite functionals on Hilbert spaces
• The Poincaré-Bendixson theorem for monotone cyclic feedback systems with delay
• Multiple periodic solutions with minimal period 4 of the delay differential equation \(\dot x(t)=-f(t,x(t-1))\)
• Morse theory for asymptotically linear Hamiltonian systems
• Proof and generalization of Kaplan-Yorke's conjecture under the condition \(F^{\prime}\) \((0) > 0\) on periodic solutions to differential delay equations
• Periodic solutions of second-order differential equations with multiple delays
• Multiple periodic solutions of differential delay equations via Hamiltonian systems. I
• Multiple periodic solutions of differential delay equations via Hamiltonian systems. II
• A periodicity theorem for autonomous functional differential equations
• Periodic solutions of nonlinear functional differential equations
• Periodic solutions of certain Lienard equations with delay
• Equivalence theorems for nonlinear operator equations and coincidence degree theory for some mappings in locally convex topological vector spaces
• Multiplicity results for periodic solutions to delay differential equations via critical point theory
• A Hopf Global Bifurcation Theorem for Retarded Functional Differential Equations
• Multiple periodic solutions of differential delay equations created by asymptotically linear Hamiltonian systems
• Periodic solutions of some differential delay equations created by Hamiltonian systems
• On the Number of Periodic Solutions to Kaplan–Yorke-like High Order Differential Delay Equations with 2k Lags
• On the Stability of a Periodic Solution of a Differential Delay Equation

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