@Article{JPDE-23-366,
author = {Alan V. Lair },
title = {Nonradial Entire Large Solutions of Semilinear Elliptic Equations},
journal = {Journal of Partial Differential Equations},
year = {2010},
volume = {23},
number = {4},
pages = {366--373},
abstract = {<p>We consider the problem of whether the equation $Δu = p(x) f (u)$ on $R^N, N ≥ 3$, has a positive solution for which $lim_{|x|→∞} u(x)=∞$ where f is locally Lipschitz continuous, positive, and nondecreasing on (0,∞) and satisfies $∫^∞_1[F(t)]^{-1/2}dt=∞$ where $F(t)=∫^t_0f(s)ds$. The nonnegative function p is assumed to be asymptotically radial in a certain sense. We show that a sufficient condition to ensure such a solution u exists is that p satisfies $∫^∞_0r\min_{|x|=r}p(x)dr=∞$. Conversely, we show that a necessary condition for the solution to exist is that p satisfies $∫^∞_0r^{1+ε}\min_{|x|=r}p(x)dr=∞$ for all $ε &gt; 0$.</p>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v23.n4.4},
url = {http://global-sci.org/intro/article_detail/jpde/5239.html}
}