关于高阶常微分方程基本解  

ON FUNDAMENTAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATION

作　　者：潘泽民[1] 程素森[1] 

机构地区：[1]包头钢铁学院数学教研室

出　　处：《包头钢铁学院学报》1989年第2期1-5,共5页Journal of Baotou University of Iron and Steel Technology

摘　　要：本文构造了高阶常微算子 L[u]=a_m(x)((d^mu)/(dx^m))+a_(m-1)(x)((d^(m-1)u)/(dx^(m-1)))+…+a_0(x)u的Hadamard基本解展式,并给出由该基本解的升维地构造高维算子的基本解。In this note, Hadamard's procedure for constructing a fundamental solution is generalized to the case of general linear holomorphic high—order ordinary differential equation L[U]=a_m(x)d^mu/dx^m+a_(m-1)(x)d^(m-1)u/dx^(m-1)+…+a_0(x)u=0 with am (x)=0 The first paragraph, We constructed charactarstic cone and invariant differential form. The next two paragraphs contain the construction the formal fundamental solution and the proof Its convergency. the same time, We gave ascending dimension construction to ordinary differenal equation's fundamental solution Lx. yU=LxU+LyU

关 键 词：高阶常微分方程 基本解 常微分方程 微分算子 

分 类 号：O175.1[理学—数学]