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.