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September  2004, 3(3): 465-474. doi: 10.3934/cpaa.2004.3.465

Nonradial blow-up solutions of sublinear elliptic equations with gradient term

Marius Ghergu 1, and  Vicenţiu Rădulescu 1,

1. 

Department of Mathematics, University of Craiova, Street A. I. Cuza No. 13, 200 585 Craiova, Romania, Romania

Received  March 2003 Revised  February 2004 Published  June 2004

Let $f$ be a continuous and non-decreasing function such that $f>0$ on $(0,\infty)$, $f(0)=0$, su$p_{s\geq 1} f(s)/s< \infty$ and let $p$ be a non-negative continuous function. We study the existence and nonexistence of explosive solutions to the equation $\Delta u+|\nabla u|=p(x)f(u)$ in $\Omega,$ where $\Omega$ is either a smooth bounded domain or $\Omega=\mathbb R^N$. If $\Omega$ is bounded we prove that the above problem has never a blow-up boundary solution. Since $f$ does not satisfy the Keller-Osserman growth condition at infinity, we supply in the case $\Omega=\mathbb R^N$ a necessary and sufficient condition for the existence of a positive solution that blows up at infinity.
Keywords: maximum principle, Explosive solution, elliptic equation, sublinear growth condition..
Mathematics Subject Classification: 35B50, 35J60, 58J0.
Citation: Marius Ghergu, Vicenţiu Rădulescu. Nonradial blow-up solutions of sublinear elliptic equations with gradient term. Communications on Pure and Applied Analysis, 2004, 3 (3) : 465-474. doi: 10.3934/cpaa.2004.3.465
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