常微分方程的广函解

On Generalized-Function Solutions of Ordinary Differential Equations

本文讨论形如sum from i=0 to n ai(t)x^(a-i)(t)=0的常微分方程的广函解。通过把问题化为代数方程。归结为对某个相关矩阵及其增广矩阵的秩的讨论,给出了m阶广函解存在的一般形式的充分必要条件,并指出了确定广函解阶数的途径。

This paper deals with the existence of generalized-function solutionsfor the ordinary differential equations of the form sum from i=1 to n(a_i(t)x^((n-i))(t))=0.By deducing the question into an algebraic equations, it is put in theanalysis for ranks of a related matrix and its augmented matrix. Asufficient and necessary condition with a general form is given for theexistence of generalized-function solutions of m-order, and the ways aregiven to determine orders of generalized-function solutions.