Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 13, pp. 1-13.
Title: Positive solutions to quasilinear equations involving
critical exponent on perturbed annular domains
Author: Claudianor O. Alves (Univ. Federal de Campina Grande, Brazil)
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 $N>p \geq 2$.
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