Bounded Solutions of Lane-Emden-Fowler system in 2D Exterior Domains

Abstract: This research investigates the Lane-Emden-Fowler sublinear system in two-dimensional exterior domains, motivated by the corresponding scalar cases studied by Constantin (1997) and Yin (2004). Utilizing Liouville transformation, Schauder's fixed point theorem and sub-supersolution method, we establish the existence of bounded positive solutions under suitable conditions on the functions involved. As citations in the papers by Constantin (1997) and Yin (2004) show, this work is the first to consider the system case.