Infinitely many periodic solutions for second order Hamiltonian systems

TL;DR

This paper proves the existence of infinitely many periodic solutions for second order Hamiltonian systems with potentials that are asymptotically quadratic or superquadratic, expanding understanding of such dynamical systems.

Contribution

It establishes the existence of infinitely many solutions for a broad class of Hamiltonian systems with specific growth conditions on the potential.

Findings

Existence of infinitely many periodic solutions proven.

Results apply to systems with asymptotically quadratic or superquadratic potentials.

Contributes to the theory of Hamiltonian systems with unbounded potentials.

Abstract

In this paper, we study the existence of infinitely many periodic solutions for second order Hamiltonian systems $\ddot{u}+\nabla_u V(t,u)=0$, where $V(t, u)$ is either asymptotically quadratic or superquadratic as $|u|\to \infty$.