A remark on the existence of entire positive solutions for a class of semilinear elliptic systems

Under the simple conditions on f and g, we show that entire positive radial solutions exist for the semilinear elliptic system Δ u = p ( | x | ) f ( v ) , Δ v = q ( | x | ) g ( u ) , x ∈ R N , N ⩾ 3 , where the functions p , q : [ 0 , ∞ ) → [ 0 , ∞ ) are continuous.