2005-Oujda International Conference on Nonlinear Analysis, Oujda, Morocco.
Electron. J. Diff. Eqns., Conference 14 (2006), pp. 149-153.

Multiplicity results for nonlinear elliptic equations

Samira Benmouloud, Mostafa Khiddi, Simohammed Sbai

Abstract:
Let $\Omega$ be a bounded domain in $\mathbb{R}^{N}$, $N\geq 3$, and $p=\frac{2N}{N-2}$ the limiting Sobolev exponent. We show that for $f\in H^1_0(\Omega)^\ast$, satisfying suitable conditions, the nonlinear elliptic problem
$$\displaylines{ -\Delta u =|u |^{ p-2 }u +f \quad \hbox{in } \Omega \cr u=0 \quad \hbox{on } \partial\Omega }$$
has at least three solutions in $H_{0}^{1}(\Omega)$.

Published September 20, 2006.
Math Subject Classifications: 35J20, 35J65.
Key Words: Semilinear elliptic equations; critical Sobolev exponent.

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Samira Benmouloud
E.G.A.L, Dépt. Maths, Fac. Sciences
Université Ibn Tofail, BP. 133, Kénitra, Maroc
email: ben.sam@netcourrier.com
  Mostafa Khiddi
E.G.A.L, Dépt. Maths, Fac. Sciences
Université Ibn Tofail, BP. 133, Kénitra, Maroc
Simohammed Sbai
E.G.A.L, Dépt. Maths, Fac. Sciences
Université Ibn Tofail, BP. 133, Kénitra, Maroc
email: sbaisimo@netcourrier.com

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