Implicit Linear Differential-Difference Equations in the Module of Formal Generalized Functions over a Commutative Ring

被引：0

作者：

Gefter S.L. ^{[1
]}

Piven’ A.L. ^{[1
]}

机构：

[1] Karazin Kharkiv National University, 4, pl. Svobody, Kharkiv

来源：

Journal of Mathematical Sciences | 2021年 / 255卷 / 4期

关键词：

D O I：

10.1007/s10958-021-05381-8

中图分类号：

学科分类号：

摘要：

We study an implicit inhomogeneous linear differential-difference equation in the module of formal generalized functions over a commutative ring. We prove the well-posedness of the equation and find the fundamental solution. We obtain a representation of a unique solution to the equation in the form of the convolution of the fundamental solution and a given formal generalized function. We also consider the inhomogeneous second order differential equation over an arbitrary commutative ring. © 2021, Springer Science+Business Media, LLC, part of Springer Nature.

引用

页码：409 / 422

页数：13

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