Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 31, pp. 1-7.

Title: Multiplicity of solutions for a quasilinear problem
       with supercritical growth
       
Author: Giovany M. Figueiredo (Univ. Federal do Para, Brazil)

Abstract: 
 The multiplicity and concentration of positive solutions are
 established for the equation
 $$
 -\epsilon^{p}\Delta_{p}u+V(z)|u|^{p-2}u=|u|^{q-2}u
 +\lambda|u|^{s-2}u \quad\hbox{in }\mathbb{R}^N,
 $$
 where $1<p<N$, $\epsilon >0$, $p<q<p^* \leq s$,
 $p^{*}=\frac{Np}{N-p}$, $\lambda\geq 0$ and $V$ is a positive
 continuous function.
 
Submitted October 26, 2005. Published March 16, 2006.
Math Subject Classifications: 35A15, 35H30, 35B40.
Key Words: Variational method; penalization method; 
           Moser iteration method.