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

journal contribution
posted on 2023-06-08, 06:43 authored by Miroslav ChlebikMiroslav Chlebik, Marek Fila, Wolfgang Reichel
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.

History

Publication status

  • Published

Journal

Nonlinear Differential Equations and Applications

ISSN

1021-9722

Publisher

Springer Verlag

Issue

3

Volume

10

Page range

329-346

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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