Positive solutions of linear elliptic equations with critical growth in the Neumann boundary condition

Chlebík, Miroslav, Fila, Marek and Reichel, Wolfgang (2003) Positive solutions of linear elliptic equations with critical growth in the Neumann boundary condition. Nonlinear Differential Equations and Applications, 10 (3). pp. 329-346. ISSN 1021-9722

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Abstract

We study the existence of positive solutions of a linear elliptic equation with critical Sobolev exponent in a nonlinear Neumann boundary condition. We prove a result which is similar to a classical result of Brezis and Nirenberg who considered a corresponding problem with nonlinearity in the equation. Our proof of the fact that the dimension three is critical uses a new Pohozaev-type identity.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Miroslav Chlebik
Date Deposited: 06 Feb 2012 20:33
Last Modified: 11 May 2012 14:34
URI: http://sro.sussex.ac.uk/id/eprint/26551
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