In this paper, we provide alternative simple proofs for some of the results in , with applications to nonlinear systems, and an extension of the necessary and sufficient condition for the Maximum Principle to some cooperative quasi-linear elliptic systems involving the $p$-Laplacian. We also show that under the same conditions, we have existence of positive solutions.
J. Fleckinger. J. Hernández. F. de Thélin. "On maximum principles and existence of positive solutions for some cooperative elliptic systems." Differential Integral Equations 8 (1) 69 - 85, 1995. https://doi.org/10.57262/die/1369143784