Infinite periodic and subharmonic solutions to a class of second-order nonlinear non-autonomous neutral functional differential equations

Abstract

In this paper, by setting up a new Hilbert space H&#422γ τ and the variational method, we finded energy functions for a class of second-order nonlinear non-autonomous neutral functional differential equations. Then by critical point and Z2-group index theory, we get the sufficient condition for the existence of infinite periodic solutions for the system. Simultaneity, we put up an open question.