Boundary blow-up  for elliptic problems involving exponential  nonlinearities with  nonlinear gradient terms and singular weights

Zhijun Zhang

doi:10.3934/cpaa.2007.6.521

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2007, Volume 6, Issue 2: 521-529. Doi: 10.3934/cpaa.2007.6.521

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Boundary blow-up for elliptic problems involving exponential nonlinearities with nonlinear gradient terms and singular weights

Zhijun Zhang^1,

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

Received: February 28, 2006

Revised: July 31, 2006

Published: May 2007

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Abstract

By a perturbation method and constructing comparison functions, we show the exact asymptotic behaviour of solutions near the boundary to nonlinear elliptic problems Δ$u\pm|\nabla u|^q=b(x)e^u,\ x \in \Omega, \ u|_{\partial \Omega}=\infty, $ where $\Omega$ is a bounded domain with smooth boundary in $\mathbb R^N$, $q \geq 0$, $b$ is non-negative in $\Omega$ and singular on $\partial\Omega$.

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Mathematics Subject Classification: Primary: 35J60, 35B25; Secondary: 35B50, 35R05.

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Boundary blow-up for elliptic problems involving exponential nonlinearities with nonlinear gradient terms and singular weights

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