Subharmonic and homoclinic solutions for second order Hamiltonian systems with new superquadratic conditions

The existence of infinitely many subharmonic solutions is obtained for a class of nonautonomous second order Hamiltonian systems with a new superquadratic condition. Furthermore, we can get the existence of homoclinic solutions as the limit of subharmonics under a stronger superquadratic condition which is still weaker than the growth conditions in the references.