Electron. J. Diff. Equ., Vol. 2010(2010), No. 96, pp. 1-11.

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

Mingzhu Wu, Zuodong Yang

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.

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  Mingzhu Wu
Institute of Mathematics, School of Mathematical Science
Nanjing Normal University
Jiangsu Nanjing 210046, China
email: wumingzhu_2010@163.com
Zuodong Yang
Institute of Mathematics, School of Mathematical Science
Nanjing Normal University
Jiangsu Nanjing 210046, China
email: zdyang_jin@263.net

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