Homoclinic solutions for a class of nonlinear second-order differential equations with time-varying delays

Abstract

In this paper, by using Mawhin's continuation theorem of coincidence degree theory, we obtain some sufficient conditions for the existence of homoclinic solutions for a class of nonlinear second-order differential equations with timevarying delays. Moreover, we give an example to illustrate the feasibility of obtained results. Our results are completely new.