Copyright © 1986 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Associated with each linear homogeneous differential equation y ( n ) = ∑ i = 0 n − 1 a i ( x ) y ( i ) of order n on the real line, there is an equivalent integral equation f ( x ) = f ( x 0 ) + ∫ x 0 x h ( u ) d u + ∫ x 0 x [ ∫ x 0 u G n − 1 ( u , v ) a 0 ( v ) f ( v ) d v ] d u which is satisfied by each solution f ( x ) of the differential equation.