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We establish the results concerning existence and non-existence of entire positive so- lutions for the nonlinear elliptic systems ⎧ ⎩ −Δpu = a(x)u m +λc(x)v n , x ∈ R N , −Δqv = b(x)v l +θc(x)u n , x ∈ R N , u,v > 0, x ∈ R N and u → 0,v → 0a s|x |→ ∞, where 1 < p,q < N and λ,θ 0 are nonnegative parameters, a,b,c : R N → (0,∞) are locally Holder continuous functions not identically zero, and −∞<m< p−1,−∞<l <q−1,max{p− 1,q −1} < n. The main purpose of this paper is to extend the principal theorem of Xu and Yang in (23) which concerned single equation.

Existence and non-existence of entire positive solutions for quasilinear systems with singular and super-linear terms