On Sharp Oscillation Criteria for General Third-Order Delay Differential Equations
In this paper, effective oscillation criteria for third-order delay differential equations of the form, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mfenced separators="" open=...
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MDPI AG
2021-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/14/1675 |
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| author | Irena Jadlovská George E. Chatzarakis Jozef Džurina Said R. Grace |
| author_facet | Irena Jadlovská George E. Chatzarakis Jozef Džurina Said R. Grace |
| author_sort | Irena Jadlovská |
| collection | DOAJ |
| description | In this paper, effective oscillation criteria for third-order delay differential equations of the form, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mfenced separators="" open="(" close=")"><msub><mi>r</mi><mn>2</mn></msub><msup><mfenced separators="" open="(" close=")"><msub><mi>r</mi><mn>1</mn></msub><msup><mi>y</mi><mo>′</mo></msup></mfenced><mo>′</mo></msup></mfenced><mo>′</mo></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>+</mo><mi>q</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>y</mi><mrow><mo>(</mo><mi>τ</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula> ensuring that any nonoscillatory solution tends to zero asymptotically, are established. The results become sharp when applied to a Euler-type delay differential equation and, to the best of our knowledge, improve all existing results from the literature. Examples are provided to illustrate the importance of the main results. |
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| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T09:32:13Z |
| publishDate | 2021-07-01 |
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| series | Mathematics |
| spelling | doaj.art-30fcb9f424d748cb903eeaeafde203d02023-11-22T04:20:31ZengMDPI AGMathematics2227-73902021-07-01914167510.3390/math9141675On Sharp Oscillation Criteria for General Third-Order Delay Differential EquationsIrena Jadlovská0George E. Chatzarakis1Jozef Džurina2Said R. Grace3Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 04001 Košice, SlovakiaDepartment of Electrical and Electronic Engineering Educators, School of Pedagogical and Technological Education (ASPETE) Marousi, 15122 Athens, GreeceDepartment of Mathematics and Theoretical Informatics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, Letná 9, 04200 Košice, SlovakiaDepartment of Engineering Mathematics, Faculty of Engineering, Cairo University, Orman, Giza 12221, EgyptIn this paper, effective oscillation criteria for third-order delay differential equations of the form, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mfenced separators="" open="(" close=")"><msub><mi>r</mi><mn>2</mn></msub><msup><mfenced separators="" open="(" close=")"><msub><mi>r</mi><mn>1</mn></msub><msup><mi>y</mi><mo>′</mo></msup></mfenced><mo>′</mo></msup></mfenced><mo>′</mo></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>+</mo><mi>q</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>y</mi><mrow><mo>(</mo><mi>τ</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula> ensuring that any nonoscillatory solution tends to zero asymptotically, are established. The results become sharp when applied to a Euler-type delay differential equation and, to the best of our knowledge, improve all existing results from the literature. Examples are provided to illustrate the importance of the main results.https://www.mdpi.com/2227-7390/9/14/1675third-order differential equationdelayproperty Aoscillation |
| spellingShingle | Irena Jadlovská George E. Chatzarakis Jozef Džurina Said R. Grace On Sharp Oscillation Criteria for General Third-Order Delay Differential Equations Mathematics third-order differential equation delay property A oscillation |
| title | On Sharp Oscillation Criteria for General Third-Order Delay Differential Equations |
| title_full | On Sharp Oscillation Criteria for General Third-Order Delay Differential Equations |
| title_fullStr | On Sharp Oscillation Criteria for General Third-Order Delay Differential Equations |
| title_full_unstemmed | On Sharp Oscillation Criteria for General Third-Order Delay Differential Equations |
| title_short | On Sharp Oscillation Criteria for General Third-Order Delay Differential Equations |
| title_sort | on sharp oscillation criteria for general third order delay differential equations |
| topic | third-order differential equation delay property A oscillation |
| url | https://www.mdpi.com/2227-7390/9/14/1675 |
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