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2007 Quasilinear elliptic equations with natural growth
Boumediene Abdellaoui, Lucio Boccardo, Ireneo Peral, Ana Primo
Differential Integral Equations 20(9): 1005-1020 (2007).

Abstract

In this paper we deal with the problem $$\left\{ \begin{array}{rcl} - {\rm div}\, (a(x,u)\nabla u) +{g(x,u,\nabla u)} & = & \lambda h(x)u + f{\mbox{ in }}\Omega,\\ u & = & 0{\mbox{ on }}\partial\Omega. \end{array} \right. $$ The main goal of the work is to get hypotheses on $a$, $g$ and $h$ such that the previous problem has a solution for all $\lambda>0$ and $f\in L^1(\Omega)$. In particular, we focus our attention in the model equation with $a(x,u)= (1+|u|^m)$, $g(x,u,\nabla u)=\frac{m}{2}|u|^{m-2}u|\nabla u|^2$ and $h(x)=\dfrac{1}{|x|^2}$.

Citation

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Boumediene Abdellaoui. Lucio Boccardo. Ireneo Peral. Ana Primo. "Quasilinear elliptic equations with natural growth." Differential Integral Equations 20 (9) 1005 - 1020, 2007.

Information

Published: 2007
First available in Project Euclid: 20 December 2012

zbMATH: 1212.35078
MathSciNet: MR2349377

Subjects:
Primary: 35J60
Secondary: 35D05 , 35D10 , 35J20 , 35J70 , 47J30

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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Vol.20 • No. 9 • 2007
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