Periodic and homoclinic solutions generated by impulses

In this paper we study the existence of periodic and homoclinic solutions for a class of second order differential equations of the form q̈+Vq(t,q)=f(t) with impulsive conditions Δq̇(sk)=gk(q(sk)) via variational methods. Our results show that under appropriate conditions such a system possesses at least one non-zero periodic solution and at least one non-zero homoclinic solution and these solutions are generated by impulses when f≡0f≡0. Furthermore, one of the results gives us a lower bound of the number of periodic solutions generated by impulses and this lower bound is determined by the number of impulses of the system in a period of the solution.