Oscillation criteria for third-order delay differential equations
Abstract The objective in this paper is to study the oscillatory and asymptotic behavior of the solutions of a linear third-order delay differential equation of the form ( r 2 ( t ) ( r 1 ( t ) y ′ ( t ) ) ′ ) ′ + q ( t ) y ( τ ( t ) ) = 0 . $$ \bigl( r_{2}(t) \bigl( r_{1}(t)y'(t) \bigr) '...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-10-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-017-1384-y |
| _version_ | 1818531874381758464 |
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| author | George E Chatzarakis Said R Grace Irena Jadlovská |
| author_facet | George E Chatzarakis Said R Grace Irena Jadlovská |
| author_sort | George E Chatzarakis |
| collection | DOAJ |
| description | Abstract The objective in this paper is to study the oscillatory and asymptotic behavior of the solutions of a linear third-order delay differential equation of the form ( r 2 ( t ) ( r 1 ( t ) y ′ ( t ) ) ′ ) ′ + q ( t ) y ( τ ( t ) ) = 0 . $$ \bigl( r_{2}(t) \bigl( r_{1}(t)y'(t) \bigr) ' \bigr) '+q(t)y \bigl(\tau(t) \bigr)= 0. $$ We establish new oscillation criteria that can be used to test for oscillations, even when the previously known criteria fail to apply. Examples illustrating the results are also given. |
| first_indexed | 2024-12-11T17:38:09Z |
| format | Article |
| id | doaj.art-05cef84a0a904c9882c98cf991052687 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-11T17:38:09Z |
| publishDate | 2017-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-05cef84a0a904c9882c98cf9910526872022-12-22T00:56:37ZengSpringerOpenAdvances in Difference Equations1687-18472017-10-012017111110.1186/s13662-017-1384-yOscillation criteria for third-order delay differential equationsGeorge E Chatzarakis0Said R Grace1Irena Jadlovská2Department of Electrical and Electronic Engineering Educators, School of Pedagogical and Technological Education (ASPETE)Department of Engineering Mathematics, Faculty of Engineering, Cairo UniversityDepartment of Mathematics and Theoretical Informatics, Faculty of Electrical Engineering and Informatics, Technical University of KošiceAbstract The objective in this paper is to study the oscillatory and asymptotic behavior of the solutions of a linear third-order delay differential equation of the form ( r 2 ( t ) ( r 1 ( t ) y ′ ( t ) ) ′ ) ′ + q ( t ) y ( τ ( t ) ) = 0 . $$ \bigl( r_{2}(t) \bigl( r_{1}(t)y'(t) \bigr) ' \bigr) '+q(t)y \bigl(\tau(t) \bigr)= 0. $$ We establish new oscillation criteria that can be used to test for oscillations, even when the previously known criteria fail to apply. Examples illustrating the results are also given.http://link.springer.com/article/10.1186/s13662-017-1384-ythird-orderdifferential equationdelayGrönwall inequalityoscillation |
| spellingShingle | George E Chatzarakis Said R Grace Irena Jadlovská Oscillation criteria for third-order delay differential equations Advances in Difference Equations third-order differential equation delay Grönwall inequality oscillation |
| title | Oscillation criteria for third-order delay differential equations |
| title_full | Oscillation criteria for third-order delay differential equations |
| title_fullStr | Oscillation criteria for third-order delay differential equations |
| title_full_unstemmed | Oscillation criteria for third-order delay differential equations |
| title_short | Oscillation criteria for third-order delay differential equations |
| title_sort | oscillation criteria for third order delay differential equations |
| topic | third-order differential equation delay Grönwall inequality oscillation |
| url | http://link.springer.com/article/10.1186/s13662-017-1384-y |
| work_keys_str_mv | AT georgeechatzarakis oscillationcriteriaforthirdorderdelaydifferentialequations AT saidrgrace oscillationcriteriaforthirdorderdelaydifferentialequations AT irenajadlovska oscillationcriteriaforthirdorderdelaydifferentialequations |