Periodic solutions of second-order differential equations with multiple delays

In this paper, we study the periodic solutions of high order differential delay equations with [Formula: see text] lags. And the [Formula: see text]-periodic solutions are obtained by using the variational method and the method of Kaplan–Yorke coupling system. This is a new type of differential delay equations compared with all previous researches. And it provides a theoretical basis for the study of differential delay equations. An example is given to demonstrate our main results.

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On the Number of Periodic Solutions to Kaplan–Yorke-like High Order Differential Delay Equations with 2k Lags

Lin

Sun

2019

Int. J. Bifurcation Chaos

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Global Bifurcation of Periodic Solutions in Symmetric Reversible Second Order Systems with Delays

Balanov

Burnett

Krawcewicz

et al. 2021

Int. J. Bifurcation Chaos

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Global bifurcation and spatio-temporal patterns of periodic solutions (with prescribed period) to second order reversible equivariant autonomous systems with commensurate delays are studied using the Brouwer/Leray–Schauder [Formula: see text]-equivariant degree theory. Here, [Formula: see text] is related to the reversal symmetry combined with the autonomous form of the system, [Formula: see text] reflects extra spacial symmetries of the system, and [Formula: see text] is related to the oddness of the right-hand side. Abstract results are supported by a concrete example with [Formula: see text] — the dihedral group of order 12.

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Multiple Periodic Solutions of Nonautonomous Delay Differential Equations

Li,

2023

Int. J. Bifurcation Chaos

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Periodic solutions of second-order differential equations with multiple delays

Abstract: By using the critical point theory and S 1 index theory, we obtain a new result for the existence and multiplicity of periodic solutions for a class of second-order delay differential equations x" (t) = f (x(t))-[f (x(t-1))+f (x(t-2))+...+f (x(t- (N -1)))].

Cited by 11 publications

References 29 publications

On the Number of Periodic Solutions to Kaplan–Yorke-like High Order Differential Delay Equations with 2k Lags

On the Number of Periodic Solutions to Kaplan–Yorke-like High Order Differential Delay Equations with 2k Lags

Global Bifurcation of Periodic Solutions in Symmetric Reversible Second Order Systems with Delays

Multiple Periodic Solutions of Nonautonomous Delay Differential Equations

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