Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 132, pp. 1-15.

Title: Existence and multiplicity of positive solutions
       for a singular problem associated to the p-Laplacian operator

Authors: Carlos Aranda (Univ. de Tarapaca, Arica, Chile)
         Tomas Godoy (Univ. Nacional de Cordoba, Argentina)

Abstract: 
 Consider the problem
 $$
 -\Delta_{p}u=g(u)  +\lambda h(u)\quad\hbox{in }\Omega
 $$
 with $u=0$ on the boundary, where $\lambda\in(0,\infty)$,
 $\Omega$ is a strictly convex bounded and $C^{2}$ domain in
 $\mathbb{R}^{N}$ with $N\geq2$, and $1<p\leq2$.
 Under suitable assumptions on $g$ and $h$
 that allow a singularity of $g$ at the origin, we show that for
 $\lambda$ positive and small enough the above problem has at least
 two positive solutions in $C(\overline{\Omega})\cap C^{1}(\Omega)$
 and that $\lambda=0$ is a bifurcation point from infinity.
 The existence of positive solutions for problems of the form
 $-\Delta_{p}u=K(x)  g(u)+\lambda h(u)+f(x)$ in $\Omega$,
 $u=0$ on $\partial\Omega$ is also studied.

Submitted June 18, 2004. Published November 16, 2004.
Math Subject Classifications: 35J60, 35J65.
Key Words: Singular problems; p-laplacian operator; 
           nonlinear eigenvalue problems.