Existence of Entire Large Positive Solutions of Semilinear Elliptic Systems
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 ∫∞0 tp(t) dt∞0 tq(t) dtα and β greater than unity, and ∫∞0 tp(t) dt=∞ and ∫∞0 tq(t) dt=∞ if neither α nor β is greater than one.
Journal of Differential Equations
Lair, A. V, & Wood, A. W. (2000). Existence of Entire Large Positive Solutions of Semilinear Elliptic Systems. Journal of Differential Equations, 164(2), 380–394. https://doi.org/10.1006/jdeq.2000.3768