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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2017, номер 1, страницы 29–38
(Mi basm437)
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Forbidden set of the rational difference equation $x_{n+1}=x_nx_{n-k}/(ax_{n-k+1}+x_n x_{n-k+1}x_{n-k})$
Julius Fergy T. Rabago Department of Mathematics and Computer Science, College of Science, University of the Philippines Baguio, Governor Pack Road, Baguio City 2600, PHILIPPINES
Аннотация:
This short note aims to answer one of the open problems raised by F. Balibrea and A. Cascales in [2]. In particular, the forbidden set of the nonlinear difference equation $x_{n+1}=x_nx_{n-k}/(ax_{n-k+1}+x_n x_{n-k+1}x_{n-k})$, where $k$ is a positive integer and $a$ is a positive constant, is found by first computing the closed form solution of the given equation. Additional results regarding the limiting properties and periodicity of its solutions are also discussed. Numerical examples are also provided to illustrate the exhibited results. Lastly, a possible generalization of the present work is offered as an open problem.
Ключевые слова и фразы:
forbidden set, closed form solution, difference equation, open problem.
Поступила в редакцию: 20.04.2016
Образец цитирования:
Julius Fergy T. Rabago, “Forbidden set of the rational difference equation $x_{n+1}=x_nx_{n-k}/(ax_{n-k+1}+x_n x_{n-k+1}x_{n-k})$”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2017, no. 1, 29–38
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/basm437 https://www.mathnet.ru/rus/basm/y2017/i1/p29
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