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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
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