On the construction of periodic solutions of kaplan-yorke type for some differential delay equations

DOI10.1080/00036819508840390zbMath0845.34073OpenAlexW2036387559WikidataQ58154100 ScholiaQ58154100MaRDI QIDQ4855050

Xue-Zhong He, Ji-Bin Li, Kondalsamy Gopalsamy

Publication date: 11 September 1996

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036819508840390

zbMATH Keywords

generalized Hamiltonian systemperiodic solution of Kaplan-Yorke typesingle-delay equationstwo-delays equations

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Periodic solutions to functional-differential equations (34K13) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items

Bifurcations of periodic solutions of delay differential equations ⋮ Periodic solutions of asymptotically linear delay differential systems via Hamiltonian systems ⋮ The existence of periodic solutions for second-order delay differential systems ⋮ Periodic solutions of delay differential systems via Hamiltonian systems ⋮ Periodic orbits for some systems of delay differential equations ⋮ Proof and generalization of Kaplan-Yorke's conjecture under the condition \(F^{\prime}\) \((0) > 0\) on periodic solutions to differential delay equations ⋮ Multiplicity results on periodic solutions to higher-dimensional differential equations with multiple delays ⋮ Periodic solutions of some differential delay equations created by Hamiltonian systems ⋮ Smoothness loss of periodic solutions of a neutral functional differential equation: On a bifurcation of the essential spectrum

Cites Work

• Exact formulae for periodic solutions of \(\dot x(t+1)=\alpha(-x(t)+bx^ 3(t))\)
• The existence of periodic solutions of the equation \(x'(t)=-f(x(t),x(t- {\tau{}}))\)
• Periodic solutions of analytic functional differential equations are analytic
• Periodic solutions of some nonlinear, autonomous functional differential equations. II
• Uniqueness and nonuniqueness of periodic solutions of x'(t)= -g(x(t-1))
• Solutions of \(\dot x(t)=-g(x(t-1))\) approach the Kaplan-Yorke orbits for odd sigmoid \(g\)
• Sur Une Equation Differentielle Fonctionnelle Analytique^*
• Periodic solutions of special differential equations: an example in non-linear functional analysis
• Wright's equation has no solutions of period four
• Unnamed Item

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