Abstract and Applied Analysis
Volume 3 (1998), Issue 3-4, Pages 411-423
doi:10.1155/S1085337598000633

Singular nonlinear elliptic equations in Rn

C.O. Alves1 , J.V. Goncalves2 and L.A. Maia2

1Departamento de Matemática e Estatística, Universidade Federal da Paraiba, Campina Grande 58109-970, PB, Brazil
 2Departamento de Matemática, Universidade de Brasília, Brasília DF 70910-900, Brazil

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.