TY - JOUR
T1 - Entire Large Solutions to Semilinear Elliptic Systems of Competitive Type
AU - Lair , Alan V.
JO - Journal of Partial Differential Equations
VL - 1
SP - 52
EP - 65
PY - 2019
DA - 2019/04
SN - 32
DO - http://doi.org/10.4208/jpde.v32.n1.4
UR - https://global-sci.org/intro/article_detail/jpde/13122.html
KW - Large solution
KW - entire solution
KW - semilinear
KW - elliptic system.
AB - <p>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.&nbsp; 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 $\lim_{|x|\rightarrow \infty}u(x) = \lim_{|x| \rightarrow \infty}v(x) = \infty$.</p>