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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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Official URL: http://dx.doi.org/10.1007/s00030-003-1037-6
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 |
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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 |