Abstract
We study the multiplicity of periodic solutions of a class of non-autonomous delay differential equations. By making full use of the Clark dual, the dual variational functional is considered. Some sufficient conditions are obtained to guarantee the existence of multiple periodic solutions.2000 Mathematics Subject Classification: 34K13; 34K18.
Highlights
The existence and multiplicity of periodic solutions of delay differential equations have been investigated since 1962
By combining with Kaplan-Yorke method, it can be used indirectly to study the existence of periodic solutions of delay differential equation [11,12,13,14,15,16]
We study multiple periodic solutions of the following non-autonomous delay differential equations x (t) = −f (t, x(t − π )), 2 (1)
Summary
1 Introduction The existence and multiplicity of periodic solutions of delay differential equations have been investigated since 1962. We study multiple periodic solutions of the following non-autonomous delay differential equations x (t) = −f (t, x(t − π )), 2 (1) Since the dimension of its negative space is finite, we define it as the Morse index of the dual variational functional.
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