Homoclinic solutions for ordinary $p$-Laplacian systems with local super-$p$ linear conditions

Abstract

The existence of homoclinic solutions is obtained for the ordinary $p$-Laplacian systems $\frac{{\rm d} }{{\rm d}t}\left(|\dot{u}(t)|^{p-2}\dot{u}(t)\right)-\nabla K(t,u(t))+\nabla W(t,u(t))=0$, as the limit of the $2kT$-periodic solutions which are obtained by the Mountain Pass Theorem, where $K(t,x)$ satisfies some sub-$p$ linear or asymptotic-$p$ linear conditions and $W(t,x)$ satisfies some local super-$p$ linear conditions.