Existence of solutions for second-order impulsive differential inclusions

In this paper, we investigate the existence and multiplicity of solutions to the following second-order impulsive Hamiltonian systems: {-(rho(x)(u)over dot)' + A(x)u is an element of partial derivative F(x, u(x)), a.e. x is an element of(0, T), Delta(rho(x)(u)over dot(i) (x(j))) = rho (x(j)(+)) (u)over dot(i) (x(j)(+)) - rho(x(j)(-))(u)over dot(i)(x(j)(-)) = I(ij()u(i)(x(j)))). i = 1,...,N, j = 1,...,I, alpha(1)(u)over dot(i)(0) - alpha(2)u(0) = 0, beta(1)(u)over dot(i)(T) + beta 2u(T) = 0, where A,TRNxN is a continuousmap form the interval [0, T] to the set of N-order symmetric matrices. Our methods are based on critical point theory for nondifferentiable functionals. Copyright (c) 2014 John Wiley & Sons, Ltd.