Infinitely many homoclinic solutions for nonautonomous p(t) p ( t ) -Laplacian Hamiltonian systems ?
By using the Symmetric Mountain Pass Theorem, we establish some existence criteria which guarantee that the second-order ordinary p(t) p ( t ) -Laplacian systems of the form d d t ( ? u ? ( t ) ? p ( t ) ? 2 u ? ( t ) ) ? a ( t ) ? u ( t ) ? p ( t ) ? 2 u ( t ) + ? W ( t , u ( t ) ) = 0 have infinitely many homoclinic solutions, where t ? R , u ? R N , p?C(R,R) p ? C ( R , R ) and p(t)>1 p ( t ) > 1 , a?C(R,R) a ? C ( R , R ) , and W?C1(RRN,R) W ? C 1 ( R  R N , R ) are non-periodic in t t .
homoclinic solutions symmetric mountain pass theorem second-order ordinary p(t) p ( t ) -laplacian systems p(t) p ( t ) p(t) p ( t ) p ( t ) variable exponent sobolev space