A topological approach to nonlocal elliptic partial differential equations on an annulus

For we consider the nonlocal ordinary differential equation subject to the Dirichlet boundary conditions . Due to the term appearing in the equation, this is a class of nonlocal differential equations. By using a novel order cone we are able to establish existence of a positive solution to this problem by means of topological fixed point theory. The preceding problem is really a special case of a more general problem that we consider – namely, the existence of a positive radially symmetric solution to the nonlocal elliptic partial differential equation subject to , for , where Ω is an annular region when .