On the existence and uniqueness of a solution to the boundary value problem for linear ordinary differential equations

Abstract

In this study, we investigate the Boundary Value Problem (BVP) for second order non-homogeneous linear differential equation with Dirichlet conditions. We derive a novel sufficient condition for the existence and uniqueness of a solution. The condition is formulated in terms of input parameters (coefficient functions and the length $l$ of the interval, where the BVP is considered), not in secondary terms as Lipschitz coefficients. We compare the obtained sufficient condition with those for non-linear BVPs and demonstrate that it covers a significantly wider class of BVPs.