Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 05, pp. 1-16.

Title: Existence of positive and sign-changing solutions for
       p-laplace equations with potentials in R^N
       
Authors: Mingzhu Wu   (Nanjing Normal Univ., Jiangsu, China)
         Zuodong Yang (Nanjing Normal Univ., Jiangsu, China)

Abstract:
 We study the perturbed equation
 $$\displaylines{
 -\varepsilon^{p}\hbox{div}(|\nabla u|^{p-2}\nabla
 u)+V(x)|u|^{p-2}u=h(x,u)+K(x)|u|^{p^*-2}u,\quad x\in \mathbb{R}^N\cr
 u(x)\to 0\quad \text{as } |x|\to\infty\,.
 }$$
 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.