A global bifurcation result for quasilinear elliptic equations in Orlicz-Sobolev spaces

Abstract

The paper is concerned with a global bifurcation result for the equation $$ -\text{div} (A(|\nabla u|) \nabla u) = g(x,u,\lambda) $$ in a general domain $\Omega$ with non necessarily radial solutions. Using a variational inequality formulation together with calculations of the Leray-Schauder degrees for mappings in Orlicz-Sobolev spaces, we show a global behavior (the Rabinowitz alternative) of the bifurcating branches.