Statement of the boundary value problem on the graph

Differential equations found in different applications, can be interpreted as equations in graphs. There is good reason to argue that the theory of such equations can be applied on a large scale, and on the other hand, the properties of the graph can be used to create a qualitative theory of such equations and methods for solving them. Using the simple properties of graphs, we can study the action of solutions of differential equations. There is reason to believe that the structure of the graph affects some important properties of the solution