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.
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
Funding statement: 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).
Acknowledgements
The author is grateful to all participants of the Perm Seminar on Functional Differential and Difference Equations for useful discussions, and to the referee of the paper for a number of essential comments.
References
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