Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 94, pp. 1-22.
Title: On nonnegative entire solutions of second-order semilinear
elliptic systems
Author: Tomomitsu Teramoto (Onomichi Univ., Hiroshima, Japan)
Abstract:
We consider the second-order semilinear elliptic system
$$
\Delta u_i=P_i(x)u_{i+1}^{\alpha_i}\quad\hbox{in }\mathbb{R}^N,
\quad i=1,2,\dots,m
$$
with nonnegative continuous functions $P_i$.
We establish nonexistence criteria of nonnegative nontrivial
entire solutions for this system. We also proved a Liouville
type theorem for nonnegative entire solutions.
Submitted February 6, 2003. Published September 9, 2003.
Math Subject Classifications: 35J60, 35B05
Key Words: Elliptic system; nonnegative entire solutions