Entire Large Solutions to Semilinear Elliptic Systems of Competitive Type

Alan V. Lair sci
2019 Journal of Partial Differential Equations  
We consider the elliptic system ∆u= p(|x|)u a v b , ∆v=q(|x|)u c v d on R n (n≥3) where a, b, c, d are nonnegative constants with max{a,d} ≤ 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|→∞ u(x) = lim |x|→∞ v(x) = ∞. AMS Subject Classifications: 35J47, 35B44 Chinese Library Classifications: O175.25
doi:10.4208/jpde.v32.n1.4 fatcat:66vnfpknnbdnvegkqnneawp2fa