Existence and Nonexistence of Entire Positive Solutions of Semilinear Elliptic Systems
We show that entire positive 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 and satisfy appropriate decay conditions at infinity. We also show that entire solutions fail to exist if the functions p and q are of slow decay.
Abstract © Elsevier
Journal of Mathematical Analysis and Applications
Wang, X., & Wood, A. W. (2002). Existence and Nonexistence of Entire Positive Solutions of Semilinear Elliptic Systems. Journal of Mathematical Analysis and Applications, 267(1), 361–368. https://doi.org/10.1006/jmaa.2001.7784