The Use of Green's Functions to Solve Some General Initial-Value Problems

Abstract

Ince [1 ] constructs a solution to an nth order comnpletely homogeneous linear differential system. His solution has continutous derivatives of order n -2 over its entire domain, with the (n t)st derivative discontinuotus at some point in the domain. In this paper, I use functions w^vhich solve initial value problemns whose differential equations are (in turn) nth order linear, nth order nonlinear and homogeneous in the dependent variable. If the equation satisfies a certain uniqueness condition, the solution is the only one. The Green's functions used here are not restricted to continuity of the first n-2 derivatives. One of the problems solved requires the solution to be a function with k cusp points (k is a positive integer greater than one). A nonsynmmetric function is obtained as the solution to a problem in which the linear nth order differential equation is complete, i.e., nonhomogeneous.