Linear differential equation with additional conditions and formulae for green's function

Abstract

In this paper, we investigate the m-order linear ordinary differential equation with m linearly independent additional conditions. We have found the solution to this problem and give the formula and the existence condition of Green's function. We compare two Green's functions for two such problems with different additional conditions and apply these results to the problems with nonlocal boundary conditions.

Keywords

• Linear ODE
• Green’s function
• Nonlocal Boundary Conditions