Entire large solutions for a class of Schrödinger systems with a nonlinear random operator

In this paper, we study the nonexistence and existence of radial large positive solutions for a class of Schrödinger systems with a nonlinear random operator under certain growth conditions. We also establish the necessary and sufficient conditions for the existence of radial large positive solutions by a successive iteration technique. The results of the paper improve and extend many previous work in this field of research.