Existence of solutions to a non‐variational singular elliptic system with unbounded weights

In this paper we prove an existence result for the following singular elliptic systemz > 0 in Ω , z ∈ W 0 1 , p( Ω ):− Δ p z = a ( x ) z q − 1u θ,u > 0 in Ω , u ∈ W 0 1 , p( Ω ):− Δ p u = b ( x ) z q u θ − 1,where Ω is a bounded open set in error N ( N ≥ 2 ), − Δ pis the p ‐laplacian operator, a ( x ) and b ( x ) are suitable Lebesgue functions and q > 0 , 0 < θ < 1 , p > 1 are positive parameters satisfying suitable assumptions.