Positive solutions for a non-variational elliptic system with singular nonlinearities

Abstract In this paper, we study the existence, nonexistence and multiplicity of positive solutions for a non-variational elliptic system involving singular nonlinearities and two parameters. First, we introduce a system equivalent to the original system, and then we employ the Leray–Schauder topological degree, the sub-supersolution method and the Blow Up method to prove our main result.