An asymptotic solution of a nonhomogeneous linear system of differential equations

Abstract

A complete asymptotic series expansion is found for the solutions of a nonhomogeneous linear system of differential equations whose coefficient matrix and forcing term are in L 1 [ t 0 , ∞ ) {L^1}[{t_0},\infty ) . Related results, which require that the coefficients satisfy certain conditional integrability conditions, are shown to be reducible by a transformation to the L 1 {L^1} case.