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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

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Sharp explicit oscillation conditions for difference equations with several delays

Kirill M. Chudinov
Published Online: 2019-10-15 | DOI: https://doi.org/10.1515/gmj-2019-2060


We consider explicit sufficient conditions for all solutions of a first-order linear difference equation with several variable delays and non-negative coefficients to be oscillatory. The conditions have the form of inequalities bounding below the upper and lower limits of the sums of coefficients over a subset of the discrete semiaxis. Our main results are oscillation tests based on a new principle for composing the estimated sums of coefficients. We also give some results in the form of examples, including a counterexample to a wrong oscillation test cited in several recent papers.

Keywords: Delay difference equation; oscillation; effective test; several delays

MSC 2010: 39A21; 34K11


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About the article

Received: 2017-09-11

Revised: 2018-01-05

Accepted: 2018-05-29

Published Online: 2019-10-15

Funding Source: Ministry of Education and Science of the Russian Federation

Award identifier / Grant number: 1.5336.2017/8.9

Funding Source: Russian Foundation for Basic Research

Award identifier / Grant number: 18-01-00928

The research is performed within the basic part of the state assignment of the Ministry of Science and Higher Education of the Russian Federation (project 1.5336.2017/8.9), and is supported by the Russian Foundation for Basic Research (project 18-01-00928).

Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2019-2060.

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