Abstract and Applied Analysis

Singular nonlinear elliptic equations in $\mathbf{R}^N$

C. O. Alves, J. V. Goncalves, and L. A. Maia

Full-text: Open access

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)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.

Article information

Source
Abstr. Appl. Anal., Volume 3, Number 3-4 (1998), 411-423.

Dates
First available in Project Euclid: 8 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1049832734

Digital Object Identifier
doi:10.1155/S1085337598000633

Mathematical Reviews number (MathSciNet)
MR1749419

Zentralblatt MATH identifier
0965.35052

Subjects
Primary: 35J60: Nonlinear elliptic equations

Keywords
singular nonlinear elliptic equations Schauder′s fixed point theorem existence uniqueness regularity positive solutions

Citation

Alves, C. O.; Goncalves, J. V.; Maia, L. A. Singular nonlinear elliptic equations in $\mathbf{R}^N$. Abstr. Appl. Anal. 3 (1998), no. 3-4, 411--423. doi:10.1155/S1085337598000633. https://projecteuclid.org/euclid.aaa/1049832734


Export citation