## On nonnegative entire solutions of second-order semilinear elliptic systems.(English)Zbl 1109.35323

Summary: We consider the second-order semilinear elliptic system $\Delta u_i=P_i(x)u_{i+1}^{\alpha_i}\quad\text{in }\mathbb {R}^N, \quad i=1,2,\dots,m$ 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.

### MSC:

 35J45 Systems of elliptic equations, general (MSC2000) 35J60 Nonlinear elliptic equations 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs

### Keywords:

Elliptic system; nonnegative entire solutions
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