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.