Homogeneous eigenvalue problems in Orlicz-Sobolev spaces

TL;DR

This paper investigates a fractional g-Laplacian eigenvalue problem in Orlicz-Sobolev spaces, establishing the existence of infinitely many eigenvalues and analyzing their stability as the fractional parameter approaches 1.

Contribution

It introduces a variational framework for fractional g-Laplacian eigenvalues in Orlicz-Sobolev spaces and proves the existence of an infinite eigenvalue sequence with stability results.

Findings

Existence of infinitely many eigenvalues

Eigenvalues' behavior as fractional parameter approaches 1

Stability of eigenvalues under parameter variation

Abstract

In this article we consider a homogeneous eigenvalue problem ruled by the fractional $g-$Laplacian operator whose Euler-Lagrange equation is obtained by minimization of a quotient involving Luxemburg norms. We prove existence of an infinite sequence of variational eigenvalues and study its behavior as the fractional parameter $s\uparrow 1$ among other stability results.