Periodic solutions of Euler-Lagrange equations with sublinear pontentials in an Orlicz-Sobolev space setting

TL;DR

This paper establishes the existence of periodic solutions for Hamiltonian systems with sublinear potentials within an Orlicz-Sobolev space framework, expanding the mathematical understanding of such systems.

Contribution

It introduces new existence results for periodic solutions of Euler-Lagrange equations with sublinear potentials in Orlicz-Sobolev spaces using variational methods.

Findings

Existence of periodic solutions proven under sublinear potential conditions

Application of calculus of variations in Orlicz-Sobolev spaces

Potential functions satisfying specific growth conditions

Abstract

In this paper, we obtain existence results of periodic solutions of hamiltonian systems in the Orlicz-Sobolev space $W^1L^{\Phi}([0,T])$. We employ the direct method of calculus of variations and we consider a potential function $F$ satisfying the inequality $|\nabla F(t,x)|\leq b_1(t) \Phi_0'(|x|)+b_2(t)$, with $b_1, b_2\in L^1$ and certain $N$-functions $\Phi_0$.