Existence of Entire Large Positive Solutions of Semilinear Elliptic Systems

Abstract

We show that entire large positive radial solutions exist for the semilinear elliptic system Δu=p(|x|)vα, Δv=q(|x|)uβ on RN, N⩾3, for positive α and β, provided that the nonnegative functions p and q are continuous, c-positive, and satisfy the decay conditions ∫∞0tp(t)dt<∞ and ∫∞0tq(t)dt<∞ for α and β greater than unity, and ∫∞0tp(t)dt=∞ and ∫∞0tq(t)dt=∞ if neither α nor β is greater than one.