Homoclinic Solutions for a Class of the Second-Order Impulsive Hamiltonian Systems

Abstract

This paper is concerned with the existence of homoclinic solutions for a class of the second order impulsive Hamiltonian systems. By employing the Mountain Pass Theorem, we demonstrate that the limit of a2kT-periodic approximation solution is a homoclinic solution of our problem.

Variational Approach to Impulsive Problems: A Survey of Recent Results

“…Theorem 36 (see [19,Theorem 1]). Assume that the following conditions hold: ( 1 ) (0) = 0 and lim | | → 0 ( ) | | = 0 for = 1, 2, .…”

“…From then on, variational methods have been widely used to study impulsive problems, such as boundary value problems, periodic solutions, and homoclinic solutions. We refer the reader to [3,[13][14][15][16][17][18][19][20][21][22].…”