Open AccessNonnegative Solutions of a Nonlinear System and Applications to Elliptic BVPs*
Author(s) -
Guangyuan Yang,
Yanqiu Chen
Publication year - 2021
Language(s) - English
DOI - 10.47260/jamb/1122
Subject(s) - mathematics , nonlinear system , cone (formal languages) , fixed point theorem , boundary value problem , mathematical analysis , type (biology) , fixed point , banach space , point (geometry) , pure mathematics , geometry , physics , algorithm , ecology , quantum mechanics , biology
In this communication, we study the existence of nonnegative solutions of anonlinear system in Banach spaces. These maps involved in the system defined oncone do not necessarily take values in the cone. Using fixed point theorems justestablished for this type of mappings, nonnegative solutions of the system areobtained and used to investigate elliptic boundary value problems (BVPs).MSC(2010): 47H10, 35J57.Keywords: Nonlinear system, Nonnegative solutions, Nowhere normal-outwardmaps, Fixed point, Elliptic BVPs.