Existence of solutions for a class of second-order Hamiltonian systems with impulsive effects

In this paper, a class of second-order Hamiltonian systems with impulsive effects are considered. We establish some sufficient conditions for the existence of solutions for the second-order Hamiltonian systems with impulsive effects {(u) overdot(t) = del F(t, u(t)), a,e,t is an element of[0, T]; u(0) - u(T) = (u) overdot(0) - (u) overdot(T) = 0, Delta(u) overdot(u) overdot(i) =(t(j)) = (u) overdot(i)(t(j)(+)) - (u) overdot(i)(t(j)(-)) = I-if (u(I)(t(j))), i = 1, 2, ..., N, j = 1, 2, ..., p, where t(0) = 0 < t(1) < t(2) < ... < t(p) < t(p+1) = T, u(t) = (u(1)(t), u(2)(t), ..., u(N)(t)) is an element of R-N, I-ij : R -> R (i = 1, 2, ..., N, j = 1, 2, ..., p) are continuous and F : [0, T] x R-N -> R. The solutions are sought by means of some critical point theorems. Finally, two examples are presented to illustrate the feasibility and effectiveness of our results. (C) 2009 Elsevier Ltd. All rights reserved.