Nonlinear Differential Equations with Distributed Delay: Some New Oscillatory Solutions
The oscillation of a class of fourth-order nonlinear damped delay differential equations with distributed deviating arguments is the subject of this research. We propose a new explanation of the fourth-order equation oscillation in terms of the oscillation of a similar well-studied second-order line...
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| Published in | Mathematics (Basel) Vol. 10; no. 6; p. 995 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Basel
MDPI AG
01.03.2022
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| Abstract | The oscillation of a class of fourth-order nonlinear damped delay differential equations with distributed deviating arguments is the subject of this research. We propose a new explanation of the fourth-order equation oscillation in terms of the oscillation of a similar well-studied second-order linear differential equation without damping. The extended Riccati transformation, integral averaging approach, and comparison principles are used to provide some additional oscillatory criteria. An example demonstrates the efficacy of the acquired criteria. |
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| AbstractList | The oscillation of a class of fourth-order nonlinear damped delay differential equations with distributed deviating arguments is the subject of this research. We propose a new explanation of the fourth-order equation oscillation in terms of the oscillation of a similar well-studied second-order linear differential equation without damping. The extended Riccati transformation, integral averaging approach, and comparison principles are used to provide some additional oscillatory criteria. An example demonstrates the efficacy of the acquired criteria. |
| Author | Almarri, Barakah Bazighifan, Omar Ali, Ali Hasan Lopes, António M. |
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| References_xml | – volume: 2012 start-page: 185242 year: 2012 ident: ref_5 article-title: Fourth-order differential equation with deviating argument publication-title: Abstr. Appl. Anal. doi: 10.1155/2012/185242 – volume: 1 start-page: 1 year: 2019 ident: ref_11 article-title: On the oscillation of fourth-order delay differential equations publication-title: Adv. Differ. Equ. – volume: 36 start-page: 168 year: 1981 ident: ref_15 article-title: On the existence of nonoscillatory solutions tending to zero at ∞ for differential equations with positive delays publication-title: Arch. Math. doi: 10.1007/BF01223686 – ident: ref_17 doi: 10.3390/math9141675 – ident: ref_2 doi: 10.3390/e23020129 – volume: 1 start-page: 1 year: 2019 ident: ref_12 article-title: Oscillation of third-order neutral differential equations with damping and distributed delay publication-title: Adv. Differ. Equ. – volume: 101 start-page: 268 year: 1984 ident: ref_9 article-title: Oscillation theorems for nth-order differential equations with deviating arguments publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(84)90066-0 – volume: 325 start-page: 54 year: 2007 ident: ref_18 article-title: Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2006.01.001 – ident: ref_20 doi: 10.14232/ejqtde.2016.1.7 – volume: 59 start-page: 291 year: 2007 ident: ref_4 article-title: Oscillation of certain fourth order functional differential equations publication-title: Ukrain. Mat. Zh. doi: 10.1007/s11253-007-0021-4 – volume: 55 start-page: 1 year: 2014 ident: ref_7 article-title: Oscillatory solutions of nonlinear fourth order differential equations with a middle term publication-title: Electron. J. Qual. Theory Differ. Equ. – volume: 5 start-page: 215 year: 2005 ident: ref_6 article-title: On the bounded oscillation of certain fourth order functional differential equations publication-title: Nonlinear Dyn. Syst. Theory – ident: ref_1 doi: 10.3390/math9040346 – ident: ref_13 doi: 10.3390/sym13081485 – volume: 2009 start-page: 7 year: 2009 ident: ref_14 article-title: Asymptotic dichotomy in a class of fourth-order nonlinear delay differential equations with damping publication-title: Abstr. Appl. Anal. doi: 10.1155/2009/484158 – volume: 35 start-page: 485 year: 2015 ident: ref_10 article-title: Oscillation criteria for third-order nonlinear delay differential equations with damping publication-title: Opuscula Math. doi: 10.7494/OpMath.2015.35.4.485 – ident: ref_19 doi: 10.3390/axioms9020039 – ident: ref_21 doi: 10.4324/9780203222898 – volume: 13 start-page: 2383 year: 2016 ident: ref_8 article-title: Oscillation Criteria for Certain Fourth-Order Nonlinear Delay Differential Equations publication-title: Mediterr. J. Math. doi: 10.1007/s00009-015-0630-3 – volume: 38 start-page: 185 year: 1999 ident: ref_3 article-title: The oscillation of higher-order differential equations with deviating arguments publication-title: Comput. Math. Appl. doi: 10.1016/S0898-1221(99)00193-5 – volume: 2021 start-page: 266 year: 2021 ident: ref_16 article-title: Riccati Technique and Oscillation of Second Order Nonlinear Neutral Delay Dynamic Equations publication-title: J. Comput. Anal. Appl. |
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| SubjectTerms | comparison theorem Criteria Damping damping term Differential equations distributed deviating arguments Food science fourth-order Mathematical analysis Nonlinear differential equations oscillation Riccati transformation |
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| Title | Nonlinear Differential Equations with Distributed Delay: Some New Oscillatory Solutions |
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