Homoclinic solutions for a class of asymptotically autonomous Hamiltonian systems with indefinite sign nonlinearities.

In this paper, we obtain the multiplicity of homoclinic solutions for a class of asymptotically autonomous Hamiltonian systems with indefinite sign potentials. The concentration-compactness principle is applied to show the compactness. As a byproduct, we obtain the uniqueness of the positive ground state solution for a class of autonomous Hamiltonian systems and the best constant for Sobolev inequality which are of independent interests. [ABSTRACT FROM AUTHOR]