On sublinear elliptic systems on bounded and thin unbounded domains

Abstract

In this paper, we demonstrate the existence of positive solutions for certain weakly coupled elliptic systems of sublinear growth under homogeneous Dirichlet boundary conditions. Our findings generalize existing results related to sublinear systems involving two weakly coupled equations, such as the Lane-Emden systems. Moreover, our results apply to both bounded domains and thin unbounded domains, defined as unbounded regions contained between two parallel hyperplanes, and accommodate some discontinuous nonlinearities.