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

We propose a method for solving a boundary value problem with a parameter under the presence of phase and integral constraints. We obtain the necessary and sufficient conditions for the solvability of 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 base 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.