On nonnegative entire solutions of second-order semilinear elliptic systems

Abstract

<p>We consider the second-order semilinear elliptic system</p> <pre>∆u_i = P_i(x) u^αi_i+1 in ℝ^N, i = 1, 2, ..., m</pre> <p>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.</p>