On nonnegative entire solutions of second-order semilinear elliptic systems

Abstract

We consider the second-order semilinear elliptic system ∆ui = Pi(x) u αi i+1 in ℝN, i = 1, 2, ..., m with nonnegative continuous functions Pi. We establish nonexistence criteria of nonnegative nontrivial entire solutions for this system. We also proved a Liouville type theorem for nonnegative entire solutions.