To the solution of a boundary value problem with a parameter for an ordinary differential equations

Abstract

We propose a method for solving a boundary value problem with a parameter under the presence of constraints for state and integral constraints. We obtain the necessary and sufficient conditions solvability for the boundary value problem with a parameter for ordinary differential equations. A method for constructing the solution to the boundary value problem with a parameter and constraints is developed by constructing minimizing sequences. The basis of the proposed method for solving the boundary value problem is the immersion principle. The immersion principle is created by finding the general solution for a class of the first kind Fredholm integral equations. As an example, the solution of the Sturm-Liouville problem for a parameter value in a prescribed interval is given.A.S. Aisagaliev, Zh.Kh. Zhunussova, To the solution of the boundary value problem with a parameter for ordinary differential equations.

Similar constructing method for solving nonhomogeneous mixed boundary value problem of n‐interval composite ode and its application

“…This method is a high‐precision numerical method and a very convenient method. Aisagaliev and Zhunussova proposed a method for solving the boundary value problem with parameters under phase constraints and integral constraints. Then they give the necessary and sufficient conditions for the solvability of the boundary value problem of ODEs.…”