2007, 2007(Special): 429-435. doi: 10.3934/proc.2007.2007.429

Multiplicity results for a singular and quazilinear equation

1. 

MIP-Ceremath, Manufacture des Tabacs-Bat C, 21, allée de Brienne, 31000 Toulouse, France, France

Received  September 2006 Revised  June 2007 Published  September 2007

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 < $p$, $p - 1$ < $q$ and $\lambda$, $\delta$ > 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 $p - 1$ < $q$.

Citation: J. Giacomoni, K. Sreeandh. Multiplicity results for a singular and quazilinear equation. Conference Publications, 2007, 2007 (Special) : 429-435. doi: 10.3934/proc.2007.2007.429
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