On the relationship between properties of solutions of difference equations and the corresponding differential equations

被引：0

作者：

Stanzhyts'kyi O.M. ^{[1
]}

Tkachuk A.M. ^{[1
]}

机构：

[1] Shevchenko Kyiv National University, Kyiv

来源：

Ukrainian Mathematical Journal | 2005年 / 57卷 / 7期

关键词：

Differential Equation; Periodic Solution; Difference Equation; Analogous Problem;

D O I：

10.1007/s11253-005-0253-0

中图分类号：

学科分类号：

摘要：

We establish conditions under which the existence of a periodic solution of a differential equation is preserved if a solution of the corresponding difference equation possesses the same property. We prove the convergence of periodic solutions of a system of difference equations to a periodic solution of a system of differential equations. Analogous problems are considered for bounded solutions. © 2005 Springer Science+Business Media, Inc.

引用

页码：1167 / 1176

页数：9

共 5 条

[1] Martynyuk D.I., Lectures on the Qualitative Theory of Difference Equations [In Russian], (1972)
[2] Ya Karasik G., On the preservation of a periodic solution under the transition from differential equations to finite-difference equations, Nauchn. Dokl. Vyssh. Shk., Ser. Fiz.-Mat. Nauk, 4, pp. 43-46, (1958)
[3] Skalkina M.A., On the relationship between the stability of solutions of differential and finite-difference equations, Prikl. Mat. Mekh., 19, 3, pp. 93-98, (1955)
[4] Ateiwi A.M., On the problem on periodic solutions of one class of systems of difference equations, Ukr. Mat. Zh., 49, 2, pp. 309-314, (1997)
[5] Babenko K.I., Foundations of Numerical Analysis [In Russian], (1986)

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