Year: 2019
Author: Alan V. Lair
Journal of Partial Differential Equations, Vol. 32 (2019), Iss. 1 : pp. 52–65
Abstract
We consider the elliptic system $\Delta u = p(|x|)u^av^b$, $\Delta v = q(|x|)u^cv^d$ on ${\bf R}^n$ ($n \geq 3$) where $a$, $b$, $c$, $d$ are nonnegative constants with $\max\{a,d\} \leq 1$, and the functions $p$ and $q$ are nonnegative, continuous, and the support of $\min\{p(r),q(r)\}$ is not compact. We establish conditions on $p$ and $q$, along with the exponents $a$, $b$, $c$, $d$, which ensure the existence of a positive entire solution satisfying $\lim_{|x|\rightarrow \infty}u(x) = \lim_{|x| \rightarrow \infty}v(x) = \infty$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v32.n1.4
Journal of Partial Differential Equations, Vol. 32 (2019), Iss. 1 : pp. 52–65
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Large solution