Solving Ordinary Differential Equations with Range Conditions. Applications

This paper introduces the problem of solving ordinary differential equations with extra linear conditions written in terms of ranges, and deals with the corresponding existence and uniqueness problems. Some methods for analyzing the existence of solutions and obtaining the set of all solutions, based on the theory of cones and polyhedra, are given. These solutions are found by first converting the problem to a system of linear algebraic equations and then applying the corresponding well-known theory for solving and discussing the existence and uniqueness of solutions of these systems. Finally, the methods are illustrated by their application to some practical examples of the beam problem.