Multiple solutions for fractional Hamiltonian systems locally defined near the origin

Abstract

. In this article, we are interested in the existence of in fi nitely many solutions for a class of fractional Hamiltonian systems where L ( t ) is neither uniformly positive de fi nite nor coercive, and W ( t , x ) is locally de fi ned and subquadratic or superquadratic near the origin with respect to x . The proof is based on variational methods and critical point theory.