Existence of A Solution For AGeneral Order Boundary ValueProblem Using TheLeray–Schauder Fixed PointTheorem

Introduction/purpose: this paper illustrates the existence of a generic green's function for a boundary value problem of arbitrary order that appears in many phenomena of heat convection, e.g. in the atmosphere, in the oceans, and on the sun's surface. methods: a fixed point theorem in the leray-schauder form has been used to establish the existence of a fixed point in the problem. results: the existence of a solution has been shown for an arbitrary order of the problem. some practical examples are proposed. conclusions: the boundary problem has a solution for an arbitrary order n.