多项式系数的齐次微分方程解的级与零点<br>The Order and Zeros of the Solutions of the Differential Equation with Polynomial Coefficients

2011 ◽  
Vol 01 (03) ◽  
pp. 214-223
Author(s):  
丁 培雄
Keyword(s):  
Differential Equation ◽  
Polynomial Coefficients

scholarly journals On integral solutions of the differential equation of infinite order with polynomial coefficients

1964 ◽  
Vol 4 (2) ◽  
pp. 203-227
Author(s):  
J. F. Korobeinik
Keyword(s):  
Differential Equation ◽  
Infinite Order ◽  
Polynomial Coefficients ◽  
Integral Solutions

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: Ю. Ф. Коробейник. О целых решениях дифференциального уравнения бесконечного порядка J. F. Korobeinik. Begalinės eilės diferencialinės lygties su polinominiais koeficientais sveikieji sprendiniai

Global solutions of linear ordinary differential equations with polynomial coefficients

1975 ◽  
Vol 344 (1636) ◽  
pp. 51-64 ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Power Series ◽  
Series Solution ◽  
Global Solutions ◽  
Linear Ordinary Differential Equation ◽  
Power Series Solution ◽  
Constructive Approach ◽  
Linear Ordinary Differential Equations ◽  
Polynomial Coefficients

A constructive approach is given, closely based on the work of Ford (1936) for continuing analytically a power series solution of a linear ordinary differential equation with polynomial coefficients outside the circle of convergence.

scholarly journals Solution of Inhomogeneous Fractional Differential Equations with Polynomial Coefficients in Terms of the Green’s Function, in Nonstandard Analysis

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1944
Author(s):  
Tohru Morita ◽  
Ken-ichi Sato
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Green’S Function ◽  
Fractional Differential Equation ◽  
Green's Function ◽  
Nonstandard Analysis ◽  
Polynomial Coefficients ◽  
Particular Solution ◽  
Fractional Differential ◽  
Detailed Derivation

Discussions are presented by Morita and Sato in Mathematics 2017; 5, 62: 1–24, on the problem of obtaining the particular solution of an inhomogeneous ordinary differential equation with polynomial coefficients in terms of the Green’s function, in the framework of distribution theory. In the present paper, a compact recipe in nonstandard analysis is presented, which is applicable to an inhomogeneous ordinary and also fractional differential equation with polynomial coefficients. The recipe consists of three theorems, each of which provides the particular solution of a differential equation for an inhomogeneous term, satisfying one of three conditions. The detailed derivation of the applications of these theorems is given for a simple fractional differential equation and an ordinary differential equation.

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