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