Sharp explicit oscillation conditions for difference equations with several delays-Reference-Cited by-同舟云学术

Sharp explicit oscillation conditions for difference equations with several delays

Published:2019-10-15 Issue:2 Volume:28 Page:207-218
ISSN:1572-9176
Container-title:Georgian Mathematical Journal
language:en
Short-container-title:

Author:

Chudinov Kirill M.¹

Affiliation:

1. Perm National Research Polytechnic University , Komsomolskiy pr. 29, 614990 Perm , Russia

Abstract

Abstract 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.

Funder

Ministry of Education and Science of the Russian Federation

Russian Foundation for Basic Research

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference25 articles.

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3. E. Braverman and B. Karpuz, On oscillation of differential and difference equations with non-monotone delays, Appl. Math. Comput. 218 (2011), no. 7, 3880–3887.

4. G. E. Chatzarakis, R. Koplatadze and I. P. Stavroulakis, Oscillation criteria of first order linear difference equations with delay argument, Nonlinear Anal. 68 (2008), no. 4, 994–1005.

5. G. E. Chatzarakis, S. Pinelas and I. P. Stavroulakis, Oscillations of difference equations with several deviated arguments, Aequationes Math. 88 (2014), no. 1–2, 105–123.

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