Multiplicity results for periodic solutions to delay differential equations via critical point theory

By Zhiming Guo, Jianshe Yu. 2005

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Abstract By the critical point theory, we study the existence and multiplicity of periodic solutions to the following system of delay differential equations: (*) x ′ ( t ) = - f ( x ( t - r ) ) , where x ∈ R n , f ∈ C ( R n , R n ) , and r > 0 is a given constant. A sufficient condition on the existence and multiplicity of periodic solutions for Eq. ( * ) is obtained. To the authors’ knowledge, this is the first time, the existence of periodic solutions to systems of delay differential equations is dealt with by using variational approaches directly.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c707a569d895d8ae436a10a6f0dba67c0d79dc20