On maximum principles and existence of positive solutions for some cooperative elliptic systems

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Abstract
In this paper, we provide alternative simple proofs for some of the results in [12], 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.

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