Nonnegative Solutions of a Nonlinear System and Applications to Elliptic BVPs*

Abstract

Abstract In this communication, we study the existence of nonnegative solutions of a nonlinear system in Banach spaces. These maps involved in the system defined on cone do not necessarily take values in the cone. Using fixed point theorems just established for this type of mappings, nonnegative solutions of the system are obtained and used to investigate elliptic boundary value problems (BVPs). MSC(2010): 47H10, 35J57. Keywords: Nonlinear system, Nonnegative solutions, Nowhere normal-outward maps, Fixed point, Elliptic BVPs.