Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 124, pp. 1-18.
Title: Infinite multiplicity of positive solutions for singular
nonlinear elliptic equations with convection term and
related supercritical problems
Author: Carlos C. Aranda (Univ. Nacional de Formosa, Argentina)
Abstract:
In this article, we consider the singular nonlinear elliptic problem
$$\displaylines{
-\Delta u = g(u)+h(\nabla u)+f(u) \quad\hbox{in }\Omega, \cr
u = 0 \quad\hbox{on }\partial\Omega.
}$$
Under suitable assumptions on $g, h, f, Omega$
that allow a singularity of g at the origin, we obtain
infinite multiplicity results. Moreover, we state infinite
multiplicity results for related boundary blow up supercritical
problems and for supercritical elliptic problems
with Dirichlet boundary condition.
Submitted August 24, 2009. Published October 01, 2009.
Math Subject Classifications: 35J25, 35J60.
Key Words: Bifurcation; degree theory; nonlinear eigenvalues
and eigenfunctions.