Existence of positive solutions for $p$--Laplacian problems with weights

Friedemann Brock; Leonelo Iturriaga; Justino Sánchez; Pedro Ubilla

doi:10.3934/cpaa.2006.5.941

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2006, Volume 5, Issue 4: 941-952. Doi: 10.3934/cpaa.2006.5.941

This issue Previous Article Stability of some waves in the Boussinesq system Next Article Approximate controllability and approximate null controllability of semilinear systems

Existence of positive solutions for $p$--Laplacian problems with weights

1.
Departamento de Matemáticas,, Universidad de Chile, Casilla 653, Santiago
2.
Departamento de Ingeniería Matemática and CMM., Universidad de Chile, Casilla 170 Correo 3, Santiago
3.
Departamento de Matemáticas, Universidad de La Serena, Casilla 559–554, La Serena
4.
Departamento de Matemáticas y C. C.,Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago

Received: December 2005

Revised: May 2006

Published: December 2006

Abstract / Introduction Related Papers Cited by

Abstract

We study the existence of positive solutions of the singular quasilinear elliptic equation

-div$(|x|^{-a p}|\nabla u|^{p-2}\nabla u)=|x|^{-(a+1)p+c}f(x,u)$ in $\Omega$

$u=0 $ on $\partial\Omega,$

where $p>1$. We use upper and lower--solutions methods, variational techniques and regularity theory.

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Mathematics Subject Classification: Primary: 35J60, 35J25, 35J70.

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