Multiplicity of positive solutions for a singular and critical elliptic problem in R2

Adimurthi, ; Giacomoni, Jacques (2006) Multiplicity of positive solutions for a singular and critical elliptic problem in R2 Communications in Contemporary Mathematics, 8 (5). pp. 621-656. ISSN 0219-1997

Full text not available from this repository.

Official URL: http://www.worldscinet.com/ccm/08/0805/S0219199706...

Related URL: http://dx.doi.org/10.1142/S0219199706002222

Abstract

In this paper, we are interested in the following singular problem: (P) {-Δu=λ(p(x)/uδ+h(x,u)e4πu2u|∂Ω=0, u > 0 in Ω in Ω ⊂ R2 where 0 < p ∈ L, λ > 0, 0< δ < 3, Ω a smooth bounded domain. We show on suitable conditions on h there exist two solutions in H10(Ω). Investigating the radial case, we are able to prove that the condition at infinity for h is optimal for getting the existence of the second solution.

Item Type:Article
Source:Copyright of this article belongs to World Scientific Publishing Co Pte Ltd.
Keywords:Singular Elliptic Equations in Two Dimensions; Critical Growth; Global Multiplicity; Variational Methods; Shooting Methods
ID Code:12038
Deposited On:10 Nov 2010 04:49
Last Modified:09 May 2011 11:37

Repository Staff Only: item control page