New existence of homoclinic orbits for a second-order Hamiltonian system ?
By using the Mountain Pass Theorem and the Symmetric Mountain Pass Theorem, we establish some existence criteria to guarantee that the second-order Hamiltonian system u ? ( t ) ? a ( t ) | u ( t ) | p ? 2 u ( t ) + ? W ( t , u ( t ) ) = 0 has at least one or infinitely many homoclinic orbits, where t ? R , u ? R N , a?C(R,R) a ? C ( R , R ) and W?C1(RRN,R) W ? C 1 ( R  R N , R ) are not periodic in t t . Our conditions on the potential W(t,x) W ( t , x ) are rather relaxed.
hamiltonian system homoclinic solutions variational methods weighted lp l p spaces lp l p lp l p l p