Large solutions of semilinear elliptic equationswith a  gradient term: existence and boundary behavior

Zhijun Zhang

doi:10.3934/cpaa.2013.12.1381

Article Contents

2013, Volume 12, Issue 3: 1381-1392. Doi: 10.3934/cpaa.2013.12.1381

This issue Previous Article Quasilinear elliptic problem with Hardy potential and singular term Next Article Multiple solutions for a class of $(p_1, \ldots, p_n)$-biharmonic systems

Large solutions of semilinear elliptic equations with a gradient term: existence and boundary behavior

Zhijun Zhang^1,

1.
Department of Mathematics and Informational Science, Yantai University, P.O. Box 264005, Yantai, Shandong

Received: March 31, 2012

Revised: June 30, 2012

Published: April 2013

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Abstract

In this paper, we study the existence and boundary behavior of solutions to boundary blow-up elliptic problems \begin{eqnarray*} \triangle u =b(x)f(u)(1+|\nabla u|^q), u\geq 0, \ x\in \Omega,\ u|_{\partial \Omega}=\infty, \end{eqnarray*} where $\Omega$ is a bounded domain with smooth boundary in $\mathbb R^N$, $q\in (0, 2]$, $b \in C^{\alpha}(\bar{\Omega})$ which is positive in $\Omega$, may be vanishing on the boundary, and $f$ is normalised regularly varying at infinity with positive index $p$ and $p+q>1$.

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Mathematics Subject Classification: Primary: 35J25, 35J65, 35J67.

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