THE EXISTENCE OF HOMOCLINIC ORBITS FOR HAMILTONIAN SYSTEMS WITH THE POTENTIALS CHANGING SIGN

This paper studies the existence of nontrival homoclinic orbits of the Hamiltonian systems $$ ddot q-L(t)q+V'(t,q)=0 $$ by using the critical point theory, where the potential $V(t,q)=b(t)W(q)$ can change sign. Under a new kind of "superquadratic" condition on $W$, some new results are obtained.