Nonexistence of positive entire solutions for a class of (p,q)(p,q)-Laplacian elliptic systems

In this work we consider the nonexistence of a positive entire solution for the quasilinear elliptic system equation(0.1)Δpu=f(x)vα,Δqv=g(x)uβ,x∈RN where p,q>1p,q>1 and α>q−1,β>p−1α>q−1,β>p−1. We study the effect of the asymptotic behavior of f(x),g(x)f(x),g(x) and solutions at infinity on the nonexistence of a positive solution for Problem (0.1). Some sufficient conditions for nonexistence are obtained.