Singular nonlinear elliptic equations in Rn

Abstract

This paper deals with existence, uniqueness and regularity of positive generalized solutions of singular nonlinear equations of the form −Δu+a(x)u=h(x)u−γ in Rn where a,h are given, not necessarily continuous functions, and γ is a positive number. We explore both situations where a,h are radial functions, with a being eventually identically zero, and cases where no symmetry is required from either a or h. Schauder's fixed point theorem, combined with penalty arguments, is exploited.

Keywords

• singular nonlinear elliptic equations
• Schauder's fixed point theorem
• existence
• uniqueness
• regularity
• positive solutions.