Singular nonlinear elliptic equations inRn

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−γinRnwherea,hare given, not necessarily continuous functions, andγis a positive number. We explore both situations wherea,hare radial functions, withabeing eventually identically zero, and cases where no symmetry is required from eitheraorh. Schauder's fixed point theorem, combined with penalty arguments, is exploited.