On the solution of boundary value problems for ordinary differential equations of order n and 2n with general boundary conditions

Abstract

We present a method for examining the existence and uniqueness and obtaining the exact solution to boundary value problems consisting of the differential equation Au = f, where A is a linear ordinary differential operator of order n, and multipoint and integral boundary conditions. We also derive a formula for computing the exact solution to even order boundary value problems encompassing the differential equation A2u = f subject to 2n general boundary conditions. The method is based on the correct extensions of operators in Banach spaces. © Springer Nature Switzerland AG 2020.