On the existence of periodic solutions for a class of non-autonomous differential delay equations

Rong Cheng, Junxiang Xu, Dongfebg Zhang

Abstract


This paper considers the existence of periodic solutions for a
class of non-autonomous differential delay equations
$$
x'(t)=-\sum_{i=1}^{n-1}f(t,x(t-i\tau)), \leqno{(*)}
$$
where $\tau> 0$ is a given
constant. It is shown that under some conditions on $f$ and by
using symplectic transformations, Floquet theory and some results
in critical point theory, the existence of single periodic
solution of the differential delay equation $(*)$ is obtained.
These results generalize previous results on the cases that the
equations are autonomous.

Keywords


Hamiltonian system; Floquet theory; symplectic transformation; periodic solution; delay equation; critical point theory

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