Existence and uniqueness of positive solution for non-variational elliptic systems

Abstract We prove the existence of solutions for strongly coupled elliptic systems in non-variational form involving second order uniformly elliptic linear operators in Ω. We also derive classes of systems having a multiplicity of solutions and the uniqueness of a solution. For this purpose, we use the Galerkin scheme in the product of Hilbert spaces. Using the comparison principle for systems of Lane-Emden we compare the obtained solutions.