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
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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 |
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