Existence and Multiplicity of Solutions for a Class of Hamiltonian Systems

We investigate a class of Hamiltonian systems -q ''(t)+(L(t)-xi)q(t)=a(t)|q(t)|(p-2)q(t)+eta f(t), q is an element of H-1(R,R-N), where (t,q)is an element of RxR(N), p>2, a is an element of C(R,(0,+infinity)), f is an element of C(R,R-N), xi,eta are real parameters, and L is an element of C(R,R-N2) is a positive definite symmetric matrix for all t is an element of R. The main technical approach is based on the Nehari manifold method combined with variational and topological methods. The obtained results extend and complement the results available in the literature.