We consider the elliptic system △u = p(|x|)u^av^b,△v=q(|x|)u^cv^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...We consider the elliptic system △u = p(|x|)u^av^b,△v=q(|x|)u^cv^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, bf c, d, which ensure the existence of a positive entire solution satisfying lim|x|→∞u(x)=lim|x|→∞v (x)=∞.展开更多
文摘We consider the elliptic system △u = p(|x|)u^av^b,△v=q(|x|)u^cv^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, bf c, d, which ensure the existence of a positive entire solution satisfying lim|x|→∞u(x)=lim|x|→∞v (x)=∞.
