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.