2005-Oujda International Conference on Nonlinear Analysis,
Oujda, Morocco.
Electronic Journal of Differential Equations,
Conference 14 (2006), pp. 149-153. 

Title: Multiplicity results for nonlinear elliptic equations

Authors: Samira Benmouloud (Univ. Ibn Tofail, Kenitra, Maroc)
         Mostafa Khiddi    (Univ. Ibn Tofail, Kenitra, Maroc)
	 Simohammed Sbai   (Univ. Ibn Tofail, Kenitra, Maroc)
 
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.