Nonexistence of positive entire solutions for a class of -Laplacian elliptic systems

In this work we consider the nonexistence of a positive entire solution for the quasilinear elliptic system (0.1) Δ p u = f ( x ) v α , Δ q v = g ( x ) u β , x ∈ R N where p , q > 1 and α > q − 1 , β > p − 1 . We study the effect of the asymptotic behavior of 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.