Electron. J. Diff. Eqns., Vol. 2003(2003), No. 94, pp. 1-22.

On nonnegative entire solutions of second-order semilinear elliptic systems

Tomomitsu Teramoto

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

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Tomomitsu Teramoto
Faculty of Economics, Management & Information Science
Onomichi University
1600 Hisayamada, Onomichi Hiroshima
722-8506, Japan
email: teramoto@onomichi-u.ac.jp

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