Generic existence of nondegenerate homoclinic solutions

Resumo

The paper focuses on the homoclinic solutions of a general second order Hamiltonian system. By applying an abstract parametric transversality result, it is shown that generically the problem admits finitely many homoclinic solutions. These solutions are nondegenerate in the sense that they correspond to nondegenerate critical points of the associated functional and depend smoothly on the vector field.