Quasilinear elliptic problem with Hardy potential and singularterm

Boumediene Abdellaoui; Ahmed Attar

doi:10.3934/cpaa.2013.12.1363

Article Contents

2013, Volume 12, Issue 3: 1363-1380. Doi: 10.3934/cpaa.2013.12.1363

This issue Previous Article Spatial decay bounds in a linearized magnetohydrodynamic channel flow Next Article Large solutions of semilinear elliptic equations with a gradient term: existence and boundary behavior

Quasilinear elliptic problem with Hardy potential and singular term

Boumediene Abdellaoui^1, and
Ahmed Attar^1,

1.
Département de Mathématiques, Université Abou Bakr Belkaïd, Tlemcen, Tlemcen 13000

Received: March 31, 2012

Revised: June 30, 2012

Published: April 2013

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Abstract

We consider the following quasilinear elliptic problem \begin{eqnarray*} -\Delta_pu =\lambda\frac{u^{p-1}}{|x|^p}+\frac{h}{u^\gamma} \quad in \quad\Omega, \end{eqnarray*} where $1 < p < N, \Omega\subset R^N$ is a bounded regular domain such that $0\in \Omega, \gamma>0$ and $h$ is a nonnegative measurable function with suitable hypotheses.
The main goal of this work is to analyze the interaction between the Hardy potential and the singular term $u^{-\gamma}$ in order to get a solution for the largest possible class of the datum $h$. The regularity of the solution is also analyzed.

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Mathematics Subject Classification: Primary: 35K15, 35K55, 35K65; Secondary: 35B05, 35B40.

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