Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 117, pp. 1-9.

Title: Existence of nontrivial solutions for singular quasilinear
       equations with sign changing nonlinearity

Author: Jagmohan Tyagi (TIFR, Sharda Nagar, India)

Abstract:
 By an application of Bonanno's three critical point theorem,
 we establish the  existence of a nontrivial solution to the problem
 $$\displaylines{
 -\Delta_p u= \mu \frac{g(x)|u|^{p-2}u}{|x|^p}
 +\lambda a(x)f(u) \quad \hbox{in }\Omega,\cr
  u =0\quad \hbox{on }\partial \Omega,
 }$$
 under some restrictions on g,a and f for certain positive
 values of $\mu$ and $\lambda$.

Submitted April 15, 2010. Published August 20, 2010.
Math Subject Classifications: 35J92, 35J75.
Key Words: p-Laplacian; singularity; multiple solutions.