Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 96, pp. 1-11.

Title: Existence and concentration of solutions for a
       p-laplace equation with potentials in R^N

Authors: Mingzhu Wu   (Nanjing Normal Univ., China)
         Zuodong Yang (Nanjing Normal Univ., China)

Abstract:
 We study the p-Laplace equation with Potentials
 $$
 -\hbox{div}(|\nabla u|^{p-2}\nabla u)+\lambda
 V(x)|u|^{p-2}u=|u|^{q-2}u,
 $$
 $u\in W^{1,p}(\mathbb{R}^N)$, $x\in \mathbb{R}^N$ where
 $2\leq p$, $p<q<p^{*}$. Using a concentration-compactness principle
 from critical point theory, we obtain existence,
 multiplicity solutions, and concentration of solutions.

Submitted January 22, 2010. Published July 15, 2010.
Math Subject Classifications: 35J25, 35J60.
Key Words: Potentials; critical point theory; concentration;
           existence; concentration-compactness; p-Laplace.