Periodic solutions of Euler-Lagrange equations in an anisotropic Orlicz-Sobolev space setting

2017/08/22 by Mazzone, Fernando D., Acinas, Sonia · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1708.06657

Abstract

In this paper we consider the problem of finding periodic solutions of certain Euler-Lagrange equations, which include, among others, equations involving the p-Laplace and, more generality, the (p,q)-Laplace operator. We employ the direct method of the calculus of variations in the framework of anisotropic Orlicz-Sobolev spaces. These spaces appear to be useful in formulating a unified theory of existence for the type of problem considered.

Cited by

• On the existence of periodic solutions for ϕ-Laplacian inclusion systems

Related

• Periodic solutions of Euler-Lagrange equations with sublinear pontentials in an Orlicz-Sobolev space setting
• Mountain pass type periodic solutions for Euler-Lagrange equations in\n anisotropic Orlicz-Sobolev space
• Existence of two periodic solutions to general anisotropic Euler-Lagrange equations
• On the existence of periodic solutions for ϕ-Laplacian inclusion systems
• An eigenvalue problem for the anisotropic Φ-Laplacian