# American Institute of Mathematical Sciences

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

 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.
Citation: Marius Ghergu, Vicenţiu Rădulescu. Nonradial blow-up solutions of sublinear elliptic equations with gradient term. Communications on Pure & Applied Analysis, 2004, 3 (3) : 465-474. doi: 10.3934/cpaa.2004.3.465
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