Improved iterative oscillation tests for first-order deviating differential equations

Improved iterative oscillation tests for first-order deviating differential equations

In this paper, improved oscillation conditions are established for the oscillation of all solutions of differential equations with non-monotone deviating arguments and nonnegative coefficients. They lead to a procedure that checks for oscillations by iteratively computing \(\lim \sup\) and \(\lim \i...

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Main Authors: George E. Chatzarakis, Irena Jadlovská
Format: Article
Language:English
Published: AGH Univeristy of Science and Technology Press 2018-01-01
Series:Opuscula Mathematica
Subjects:
differential equation
non-monotone argument
oscillatory solution
nonoscillatory solution
Online Access:http://www.opuscula.agh.edu.pl/vol38/3/art/opuscula_math_3815.pdf
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spelling doaj-028af20a7a534a0fb672b6062e13dd622020-11-24T23:53:28ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742018-01-01383327356https://doi.org/10.7494/OpMath.2018.38.3.3273815Improved iterative oscillation tests for first-order deviating differential equationsGeorge E. Chatzarakis0Irena Jadlovská1School of Pedagogical and Technological Education (ASPETE), Department of Electrical and Electronic Engineering Educators, 14121, N. Heraklio, Athens, GreeceTechnical University of Košice, Faculty of Electrical Engineering and Informatics, Department of Mathematics and Theoretical Informatics, Letná 9, 042 00 Košice, SlovakiaIn this paper, improved oscillation conditions are established for the oscillation of all solutions of differential equations with non-monotone deviating arguments and nonnegative coefficients. They lead to a procedure that checks for oscillations by iteratively computing \(\lim \sup\) and \(\lim \inf\) on terms recursively defined on the equation's coefficients and deviating argument. This procedure significantly improves all known oscillation criteria. The results and the improvement achieved over the other known conditions are illustrated by two examples, numerically solved in MATLAB.http://www.opuscula.agh.edu.pl/vol38/3/art/opuscula_math_3815.pdfdifferential equationnon-monotone argumentoscillatory solutionnonoscillatory solution
collection DOAJ
language English
format Article
sources DOAJ
author George E. Chatzarakis
Irena Jadlovská
spellingShingle George E. Chatzarakis
Irena Jadlovská
Improved iterative oscillation tests for first-order deviating differential equations
Opuscula Mathematica
differential equation
non-monotone argument
oscillatory solution
nonoscillatory solution
author_facet George E. Chatzarakis
Irena Jadlovská
author_sort George E. Chatzarakis
title Improved iterative oscillation tests for first-order deviating differential equations
title_short Improved iterative oscillation tests for first-order deviating differential equations
title_full Improved iterative oscillation tests for first-order deviating differential equations
title_fullStr Improved iterative oscillation tests for first-order deviating differential equations
title_full_unstemmed Improved iterative oscillation tests for first-order deviating differential equations
title_sort improved iterative oscillation tests for first-order deviating differential equations
publisher AGH Univeristy of Science and Technology Press
series Opuscula Mathematica
issn 1232-9274
publishDate 2018-01-01
description In this paper, improved oscillation conditions are established for the oscillation of all solutions of differential equations with non-monotone deviating arguments and nonnegative coefficients. They lead to a procedure that checks for oscillations by iteratively computing \(\lim \sup\) and \(\lim \inf\) on terms recursively defined on the equation's coefficients and deviating argument. This procedure significantly improves all known oscillation criteria. The results and the improvement achieved over the other known conditions are illustrated by two examples, numerically solved in MATLAB.
topic differential equation
non-monotone argument
oscillatory solution
nonoscillatory solution
url http://www.opuscula.agh.edu.pl/vol38/3/art/opuscula_math_3815.pdf
work_keys_str_mv AT georgeechatzarakis improvediterativeoscillationtestsforfirstorderdeviatingdifferentialequations
AT irenajadlovska improvediterativeoscillationtestsforfirstorderdeviatingdifferentialequations
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