Monotonicity results of solutions to the uniformly elliptic nonlocal Bellman system

Abstract

In this paper, we consider the uniformly elliptic nonlocal Bellman problem $\left(\begin{array}{cc}& F_{s}u\left(x\right)=f(u\left(x\right),v\left(x\right)),\\ & F_{s}v\left(x\right)=g(u\left(x\right),v\left(x\right)).\end{array}\right)$Firstly, we study narrow region principles for the uniformly elliptic nonlocal Bellman operators in bounded and unbounded domains, which play key roles in obtaining the main results by the process of sliding method. Then we deal with monotonicity properties of solutions to the uniformly elliptic nonlocal Bellman system.