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

Vy Khoi Le

DOI: http://dx.doi.org/10.12775/TMNA.2000.022

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.

Keywords


Global bifurcation; variational inequality; Orlicz-Sobolev space; Leray-Schauder degree

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