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

Sonia Acinas; Fernando Mazzone

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ArticleOriginal scientific text

Title

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

Authors ,

Abstract

In this paper, we obtain existence results of periodic solutions of hamiltonian systems in the Orlicz-Sobolev space

W^{1} L^{Φ} ([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) Φ_{0}^{'} (| x |) + b_{2} (t)

, with

b_{1}, b_{2} \in L^{1}

and certain

N

-functions

Φ_{0}

.

Keywords

ENG

Periodic solution, Orlicz-Sobolev spaces, Euler-Lagrange,

N

-function, critical points

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Title

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

Abstract

Keywords

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