Volume 32, Issue 1
Entire Large Solutions to Semilinear Elliptic Systems of Competitive Type

Alan V. Lair

10.4208/jpde.v32.n1.4

J. Part. Diff. Eq., 32 (2019), pp. 52-65.

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  • 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 $\lim_{|x|\rightarrow \infty}u(x) = \lim_{|x| \rightarrow \infty}v(x) = \infty$.

  • History

Published online: 2019-04

  • AMS Subject Headings

35J47, 35B44

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