Homoclinic orbits for a class of second-order Hamiltonian systems with concave-convex nonlinearities

Abstract

In this paper, we study the existence of multiple homoclinic solutions for the following second order Hamiltonian systems \begin{equation*} \ddot{u}(t)-L(t)u(t)+\nabla W(t,u(t))=0, \end{equation*} where $L(t)$ satisfies a boundedness assumption which is different from the coercive condition and $W$ is a combination of subquadratic and superquadratic terms.

Keywords

• multiple homoclinic solutions
• concave--convex nonlinearities
• second-order hamiltonian systems
• bounded potential
• variational methods