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Exploring Nonoscillatory Solutions in Second-Order Neutral Differential Equations with Distributed Deviating Arguments.

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Title: Exploring Nonoscillatory Solutions in Second-Order Neutral Differential Equations with Distributed Deviating Arguments.
Authors: CINA, Bengu1 bengu58cina@gmail.com, SENEL, M. Tamer2, CANDAN, Tuncay3
Source: Gazi University Journal of Science. 2026, Vol. 39 Issue 1, p442-450. 9p.
Subjects: Existence theorems, Differential equations, Fixed point theory, Nonlinear differential equations, Delay differential equations, Biomathematics
Abstract: The occurrence of oscillation and non-oscillation is common across various models in real-world applications. For instance, impulsive partial neutral differential equations in mathematical biology and biomathematics often display both oscillatory and non-oscillatory solutions. In our investigation, we establish specific criteria that guarantee the presence of non-oscillatory solutions for variable coefficient nonlinear second-order neutral differential equations with distributed deviating arguments and a forcing term. In this work, we obtained an extension of some existing results in the literature. Using the Banach contraction principle, we obtained new sufficient conditions of existence conditions. The proof of positive solutions was provided by showing the existence of a fixed point. At the end of the paper, we give an example showing how we apply one of the theorems we have learnt. [ABSTRACT FROM AUTHOR]
Copyright of Gazi University Journal of Science is the property of Gazi University Journal of Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Exploring Nonoscillatory Solutions in Second-Order Neutral Differential Equations with Distributed Deviating Arguments.
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  Data: <searchLink fieldCode="AR" term="%22CINA%2C+Bengu%22">CINA, Bengu</searchLink><relatesTo>1</relatesTo><i> bengu58cina@gmail.com</i><br /><searchLink fieldCode="AR" term="%22SENEL%2C+M%2E+Tamer%22">SENEL, M. Tamer</searchLink><relatesTo>2</relatesTo><br /><searchLink fieldCode="AR" term="%22CANDAN%2C+Tuncay%22">CANDAN, Tuncay</searchLink><relatesTo>3</relatesTo>
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  Data: <searchLink fieldCode="JN" term="%22Gazi+University+Journal+of+Science%22">Gazi University Journal of Science</searchLink>. 2026, Vol. 39 Issue 1, p442-450. 9p.
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  Data: <searchLink fieldCode="DE" term="%22Existence+theorems%22">Existence theorems</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+equations%22">Differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Fixed+point+theory%22">Fixed point theory</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+differential+equations%22">Nonlinear differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Delay+differential+equations%22">Delay differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Biomathematics%22">Biomathematics</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: The occurrence of oscillation and non-oscillation is common across various models in real-world applications. For instance, impulsive partial neutral differential equations in mathematical biology and biomathematics often display both oscillatory and non-oscillatory solutions. In our investigation, we establish specific criteria that guarantee the presence of non-oscillatory solutions for variable coefficient nonlinear second-order neutral differential equations with distributed deviating arguments and a forcing term. In this work, we obtained an extension of some existing results in the literature. Using the Banach contraction principle, we obtained new sufficient conditions of existence conditions. The proof of positive solutions was provided by showing the existence of a fixed point. At the end of the paper, we give an example showing how we apply one of the theorems we have learnt. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Gazi University Journal of Science is the property of Gazi University Journal of Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.35378/gujs.1438589
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      – Code: eng
        Text: English
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        PageCount: 9
        StartPage: 442
    Subjects:
      – SubjectFull: Existence theorems
        Type: general
      – SubjectFull: Differential equations
        Type: general
      – SubjectFull: Fixed point theory
        Type: general
      – SubjectFull: Nonlinear differential equations
        Type: general
      – SubjectFull: Delay differential equations
        Type: general
      – SubjectFull: Biomathematics
        Type: general
    Titles:
      – TitleFull: Exploring Nonoscillatory Solutions in Second-Order Neutral Differential Equations with Distributed Deviating Arguments.
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            – D: 01
              M: 01
              Text: 2026
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