Green’s functional for higher-order ordinary differential equations with general nonlocal conditions and variable principal coefficient

Abstract

The method of Green’s functional is a little-known technique for the construction of fundamental solutions to linear ordinary differential equations (ODE) with nonlocal conditions. We apply this technique to a higher order linear ODE involving general nonlocal conditions. A novel kind of adjoint problem and Green’s functional are constructed for the completely inhomogeneous problem. Several illustrative applications of the theoretical results are provided.