Maximum principle and existence of solutions for non-necessarily cooperative systems involving Schrödinger operators

Abstract

In this paper, we obtain the necessary and sufficient conditions for having the maximum principle and existence of positive solutions for some cooperative systems involving Schrödinger operators defined on unbounded domains. Then, we deduce the existence of solutions for semi-linear systems. Finally we discuss the generalized maximum principle (q-positivity) for non-cooperative systems.

An extension of maximum principle with some applications

“…They obtained some necessary and sufficient conditions for having a maximum principle. In [33], Serag and Qamlo obtained some necessary and sufficient conditions for having the maximum principle and existence of positive solutions for some cooperative systems involving Schrödinger operators defined on unbounded domains. Then, they deduced the existence of solutions for semi-linear systems.…”