Abstract and Applied Analysis
Volume 3 (1998), Issue 3-4, Pages 411-423

Singular nonlinear elliptic equations in Rn

C. O. Alves,1 J. V. Goncalves,2 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

Received 8 April 1998

Copyright © 1998 C. O. Alves et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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)uγ 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.