Electron. J. Diff. Equ., Vol. 2010(2010), No. 117, pp. 1-9.

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

Jagmohan Tyagi

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.

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Jagmohan Tyagi
TIFR Centre For Applicable Mathematics
Post Bag No.-6503, Sharda Nagar
Chikkabommasandra, Bangalore-560065, Karnataka, India
email: jagmohan.iitk@gmail.com, jtyagi1@gmail.com

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