# American Institute of Mathematical Sciences

December  2006, 5(4): 941-952. doi: 10.3934/cpaa.2006.5.941

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

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

Received  December 2005 Revised  May 2006 Published  September 2006

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.

Citation: Friedemann Brock, Leonelo Iturriaga, Justino Sánchez, Pedro Ubilla. Existence of positive solutions for $p$--Laplacian problems with weights. Communications on Pure & Applied Analysis, 2006, 5 (4) : 941-952. doi: 10.3934/cpaa.2006.5.941
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