Homogeneous eigenvalue problems in Orlicz-Sobolev spaces

Abstract

In this article we consider a homogeneous eigenvalue problem ruledby the fractional g−Laplacian operator whose Euler-Lagrange equation is obtainedby minimization of a quotient involving Luxemburg norms. We prove existenceof an infinite sequence of variational eigenvalues and study its behavior as thefractional parameter s ↑ 1 among other stability results.