Multiplicity of homoclinic solutions for second-order Hamiltonian systems

Abstract

By using a modified function technique and variational methods, we establish the existence of infinitely many homoclinic solutions for a second-order Hamiltonian system $ddot{u}-L(t)u+F_u(t,u)=0$, for all t in R, where no coercive condition for F(t,u) at infinity is imposed.

Keywords

• Second order Hamilton system
• Homoclinic solution
• variational method