Homogeneous eigenvalue problems in Orlicz-Sobolev spaces

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.