Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 61, pp. 1-12.

Title: Three solutions for singular p-Laplacian type equations
 
Authors: Zhou Yang  (South China Normal Univ., Guangzhou, China)
         Di Geng    (South China Normal Univ., Guangzhou, China)
	 Huiwen Yan (South China Normal Univ., Guangzhou, China)

Abstract: 
 In this paper, we consider the  singular $p$-Laplacian type equation
 $$\displaylines{
  -\hbox{div}(|x|^{-\beta} a(x,\nabla u))
 =\lambda f(x,u),\quad \hbox{in }\Omega,\cr
 u=0,\quad \hbox{on }\partial\Omega,
 }$$
 where $0\leq\beta<N-p$, $\Omega$ is a smooth bounded domain in
 $\mathbb{R}^N$  containing the origin, $f$ satisfies some growth
 and singularity conditions. Under some mild assumptions on $a$,
 applying the three critical points theorem developed
 by Bonanno, we establish the existence of at least three distinct
 weak solutions to the above  problem if $f$ admits some
 hypotheses on the behavior at $u=0$ or  perturbation property.
 
Submitted January 14, 2008. Published April 22, 2008.
Math Subject Classifications: 35J60.
Key Words: p-Laplacian operator; singularity; multiple solutions.