Electron. J. Diff. Eqns., Vol. 2006(2006), No. 31, pp. 1-7.

Multiplicity of solutions for a quasilinear problem with supercritical growth

Giovany M. Figueiredo

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 less than p less than N, $\epsilon$ greater than 0, p lesss than q less than $p^* \leq s$, $p^{*}=\frac{Np}{N-p}$, $\lambda\geq 0$ 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.

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Giovany M. Figueiredo
Universidade Federal do Pará
CEP 66.075-110, Bel&eaccute;m-Pará, Brazil
email: giovany@ufpa.br

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