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2008 Existence of solution for a anisotropic equation with critical exponent
Claudianor Oliveira Alves, Abdallah El Hamidi
Differential Integral Equations 21(1-2): 25-40 (2008).

Abstract

Using variational methods we establish existence of nontrivial solutions for the following class of anisotropic critical problem $$ {(P_{\lambda})} \qquad \left \{ \begin{array}{l} - \displaystyle \sum_{i=1}^{N} \frac{\partial}{\partial x_{i}} \Big ( \Big | \frac{\partial u}{\partial x_{i}} \Big |^{p_{i}-2}\frac{\partial u}{\partial x_{i}} \Big )= \lambda f(u) + g(u) , \quad \mbox{in} \quad \Omega \\ u \geq 0, \quad \mbox{in} \quad \Omega \\ u=0, \quad \mbox{on} \quad \partial \Omega , \end{array} \right. $$ where $\Omega$ is a bounded domain with smooth boundary in $\mathbb{R}^N$, $\lambda$ is a positive parameter, $g(u)$ behaves like $|u|^{p^*-2}u$, $p^{*}$ is the critical exponent for this class of problem and $f$ is a continuous function verifying some adequate assumptions.

Citation

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Claudianor Oliveira Alves. Abdallah El Hamidi. "Existence of solution for a anisotropic equation with critical exponent." Differential Integral Equations 21 (1-2) 25 - 40, 2008.

Information

Published: 2008
First available in Project Euclid: 20 December 2012

zbMATH: 1224.35148
MathSciNet: MR2479660

Subjects:
Primary: 35J60
Secondary: 35B05, 35B33, 35J20, 47J30, 58E05

Rights: Copyright © 2008 Khayyam Publishing, Inc.

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Vol.21 • No. 1-2 • 2008
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