@Article{JPDE-32-52, author = {Lair , Alan V.}, title = {Entire Large Solutions to Semilinear Elliptic Systems of Competitive Type}, journal = {Journal of Partial Differential Equations}, year = {2019}, volume = {32}, number = {1}, pages = {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 $\lim_{|x|\rightarrow \infty}u(x) = \lim_{|x| \rightarrow \infty}v(x) = \infty$.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v32.n1.4}, url = {http://global-sci.org/intro/article_detail/jpde/13122.html} }