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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2018-01-01
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| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | http://www.opuscula.agh.edu.pl/vol38/3/art/opuscula_math_3815.pdf |
| _version_ | 1818854384954507264 |
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| author | George E. Chatzarakis Irena Jadlovská |
| author_facet | George E. Chatzarakis Irena Jadlovská |
| author_sort | George E. Chatzarakis |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-19T07:51:52Z |
| format | Article |
| id | doaj.art-028af20a7a534a0fb672b6062e13dd62 |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-19T07:51:52Z |
| publishDate | 2018-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-028af20a7a534a0fb672b6062e13dd622022-12-21T20:30:07ZengAGH 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 |
| 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 |
| title | 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_short | Improved iterative oscillation tests for first-order deviating differential equations |
| title_sort | improved iterative oscillation tests for first order deviating differential equations |
| 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 |