Electron. J. Diff. Equ., Vol. 2010(2010), No. 05, pp. 1-16.

Existence of positive and sign-changing solutions for p-laplace equations with potentials in R^N

Mingzhu Wu, Zuodong Yang

Abstract:
We study the perturbed equation
$$\displaylines{
 -\varepsilon^{p}\hbox{div}(|\nabla u|^{p-2}\nabla
 u)+V(x)|u|^{p-2}u=h(x,u)+K(x)|u|^{p^*-2}u,\quad x\in \mathbb{R}^N\cr
 u(x)\to 0\quad \hbox{as } |x|\to\infty\,.
 }$$
where $2\leq p<N$, $p^*={\frac{pN}{N-p}}$, $p<q<p^*$. Under proper conditions on $V(x)$ and $h(x,u)$, we obtain the existence and multiplicity of solutions. We also study the existence of solutions which change sign.

Submitted July 23, 2009. Published January 13, 2010.
Math Subject Classifications: 35J25, 35J60.
Key Words: Potential; critical point theory; p-Laplace; sign changing solution; multiplicity of solutions; concentration-compactness.

Show me the PDF file (286 KB), TEX file, and other files for this article.

  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.
College of Zhongbei, Nanjing Normal University
Jiangsu Nanjing 210046, China
email: zdyang_jin@263.net

Return to the EJDE web page