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Linear inhomogeneous difference equations. (Linejnye neodnorodnye raznostnye uravneniya). (Russian) Zbl 0623.39001
Moskva: “Nauka” Glavnaya Redaktsiya Fiziko-Matematicheskoj Literatury. 128 p. R. 0.85 (GOE: 86 A 6682) (1986).
Consider the linear inhomogeneous difference equations \[ (*)\quad K[y(x)]\equiv \sum^{m}_{k=0}p_ k(x)y(x+h_ k)=F(x) \] where \(p_ k(x)\), F(x) are given functions and \(h_ k\) is the deviation. Let \(h_ k\) be fixed and x be a complex variable. The authors construct and investigate partial solutions of equation (*) with linear coefficients (i.e. \(p_ k(x)=a_ kx+b_ k)\) under different assumptions on F(x). This book is a continuation of the authors’ previous publication [Linear homogeneous difference equations (1981; Zbl 0513.39002)] and is based on their research. As in the first book the authors use the Laplace integral as principle tool for constructing and investigating solutions. Some states of the theory of equations with whole differences \((h_ k=k)\) are mentioned. Theoretical statements are illustrated by examples and some applications are given.
Reviewer: M.Shahin

39A10 Additive difference equations
39-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to difference and functional equations
44A10 Laplace transform