%0 Journal Article
%T Existence and multiplicity of positive solutions for a singular problem associated to the p-Laplacian operator
%A Carlos Aranda
%A Tomas Godoy
%J Electronic Journal of Differential Equations
%D 2004
%I Texas State University
%X Consider the problem $$ -Delta_{p}u=g(u) +lambda h(u)quadhbox{in }Omega $$ with $u=0$ on the boundary, where $lambdain(0,infty)$, $Omega$ is a strictly convex bounded and $C^{2}$ domain in $mathbb{R}^{N}$ with $Ngeq2$, and 1 less than $pleq2$. 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 $partialOmega$ is also studied.
%K Singular problems
%K p-laplacian operator
%K nonlinear eigenvalue problems.
%U http://ejde.math.txstate.edu/Volumes/2004/132/abstr.html