Existence of entire large positive solutions of a semilinear elliptic system

摘要

We show that large positive radial solutions exist for the semilinear elliptic system Δu=p(|x|)f(v), Δv=q(|x|)g(u) on RN(N⩾3) for nonnegative, nondecreasing continuous functions f and g. Provided the nonnegative functions p and q are continuous, C-positive and satisfy the decay conditions ∫∞0tp(t)dt<∞ and ∫∞0tq(t)dt<∞, and f, g satisfy ∫∞1[∫s0f(t)dt]−(1/2)ds<∞, ∫∞1[∫s0g(t)dt]−(1/2)ds<∞.