Electron. J. Diff. Equ., Vol. 2009(2009), No. 124, pp. 1-18.

Infinite multiplicity of positive solutions for singular nonlinear elliptic equations with convection term and related supercritical problems

Carlos C. Aranda

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 1, 2009.
Math Subject Classifications: 35J25, 35J60.
Key Words: Bifurcation; degree theory; nonlinear eigenvalues and eigenfunctions.

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Carlos C. Aranda
Laboratorio de modelización, cálculo numérico y diseno experimental
Facultad de Recursos Naturales
Universidad Nacional de Formosa, Argentina
email: carloscesar.aranda@gmail.com

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