Electron. J. Diff. Eqns., Vol. 2005(2005), No. 13, pp. 1-13.

Positive solutions to quasilinear equations involving critical exponent on perturbed annular domains

Claudianor O. Alves

Abstract:
In this paper we study the existence of positive solutions for the problem
$$ -\Delta_{p}u=u^{p^{*}-1} \quad \hbox{in } \Omega \quad \hbox{and} \quad u=0 \quad \hbox{on } \partial{\Omega} $$
where $\Omega$ is a perturbed annular domain (see definition in the introduction) and $N greater than p \geq 2$. To prove our main results, we use the Concentration-Compactness Principle and variational techniques.

Submitted August 5, 2004. Published January 30, 2005.
Math Subject Classifications: 35B33, 35H30.
Key Words: p-Laplacian operator; critical exponents; deformation lemma

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Claudianor O. Alves
Universidade Federal de Campina Grande
Departamento de Matemática e Estatística
CEP 58109-970 Campina Grande - PB, Brazil
email: coalves@dme.ufpb.br

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