Periodic solutions of the second order damped systems with singularities and deviating arguments

摘要

In this paper, we study the existence of periodic solutions of the second order damped systems with singularities and deviating argumentsx″+p1(t)x′+q1(t)x=f1(t,y(t-τ1(t)))+e1(t),y″+p2(t)y′+q2(t)y=f2(t,x(t-τ2(t)))+e2(t),where pi,qi,τi,ei∈L1(R) are T-periodic, fi∈Car(R×R+,R+) (i=1,2) are T-periodic with the first variable and have singularities at the origin. We prove that the singularities of fi enable the existence of periodic solutions by using Schauder’s fixed point theorem.