Multiplicity results for a singular and quazilinear equation

In this paper, we investigate the following quasilinear and singular problem: -$\Delta_pu = \lambda/(u^\delta) + u^q$ in $\Omega$ $u|_(\partial\Omega) = 0 , u > 0$ in $\Omega$ (1) where $\Omega$ is an open bounded domain with smooth boundary, 1 0. We first prove that there exist weak solutions for $\lambda$ > 0 small in $W^(1,p)_0(\Omega) \cap C(bar(\Omega))$ if and only if $\delta < 2 + 1/(p - 1)$ . Investigating the radial symmetric case $(\Omega = B_R(0))$, we prove by a shooting method the global multiplicity of solutions to $(P)$ in $C(bar(\Omega))$ with $0 < \delta$, 1 < $p$ and $p - 1$ < $q$.