New conditions on homoclinic solutions for a subquadratic second order Hamiltonian system
New conditions on homoclinic solutions for a subquadratic second order Hamiltonian system
In this paper, we deal with the second-order Hamiltonian system $$ (*)\quad\ddot{u}-L(t)u+\nabla W(t, u)=0. $$ We establish some criteria which guarantee that the above system has at least one or infinitely many homoclinic solutions under the assumption that $W(t, x)$ is subquadratic at infinity and $L(t)$ is a real symmetric …