Existence of homoclinic orbits for a class of asymptotically p-linear aperiodic p-Laplacian systems

Abstract

By applying a variant version of Mountain Pass Theorem in critical point theory, the existence of homoclinic solutions is obtained for the following asymptotically p-linear aperiodic p-Laplacian systemddt(|u˙(t)|p-2u˙(t))+∇[-K(t,u(t))+W(t,u(t))]=0,where p∈(1,+∞),t∈R,u∈RN,K,W∈C1(R×RN,R) are not periodic in t and W is asymptotically p-linear at infinity.