Infinitely many homoclinic solutions for a class of subquadratic second-order Hamiltonian systems

TL;DR

This paper proves the existence of infinitely many homoclinic solutions for a class of subquadratic second-order Hamiltonian systems with indefinite linear parts and subquadratic growth in the potential, using variational methods.

Contribution

It establishes the existence of infinitely many solutions for systems with indefinite linear parts and subquadratic potentials, extending previous results to more general conditions.

Findings

Existence of infinitely many homoclinic solutions proven.

Applicable to systems with indefinite linear operators.

Handles potentials with growth rate between 1 and 1.5.

Abstract

In this paper, we mainly consider the existence of infinitely many homoclinic solutions for a class of subquadratic second-order Hamiltonian systems $\ddot{u}-L(t)u+W_u(t,u)=0$, where $L(t)$ is not necessarily positive definite and the growth rate of potential function $W$ can be in $(1,3/2)$. Using the variant fountain theorem, we obtain the existence of infinitely many homoclinic solutions for the second-order Hamiltonian systems.