Oscillation Criteria for Solutions of Neutral Differential Equations of the Second-Order Emden-Fowler Type with Forcing Term
In this paper, the oscillation property and the asymptotic behavior of solutions of neutral second-order differential Equations of the Emden-Fowler type were studied under the influence of the coefficients of forces. It has been shown through this research that the coefficients of forces in additi...
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University of Baghdad
2025-01-01
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| Series: | Ibn Al-Haitham Journal for Pure and Applied Sciences |
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| Online Access: | https://jih.uobaghdad.edu.iq/index.php/j/article/view/3515 |
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| author | Jihan Saad Hussain Ali Mohamad |
| author_facet | Jihan Saad Hussain Ali Mohamad |
| author_sort | Jihan Saad |
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In this paper, the oscillation property and the asymptotic behavior of solutions of neutral second-order differential Equations of the Emden-Fowler type were studied under the influence of the coefficients of forces. It has been shown through this research that the coefficients of forces in addition to the Emden-Fowler type have a major role on the oscillation of solutions of neutral Equations. As well as its effect on the convergence and divergence of nonoscillatory solutions. For this purpose, some conditions are obtained to ensure that all solutions of the neutral Equations Emden-Fowler type oscillating or nonoscillating go to ∞, as t → ∞. Some of these conditions are the development of conditions similar to them in some of the well-known results included in the references, for example, condition (8) in this research with condition (4) in (9). The obtained results included some illustrative examples showing that the resulting conditions are easy to apply and guarantee oscillation.
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| format | Article |
| id | doaj-art-82f79a72483942b89ed6d9310d3a9d22 |
| institution | Kabale University |
| issn | 1609-4042 2521-3407 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | University of Baghdad |
| record_format | Article |
| series | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| spelling | doaj-art-82f79a72483942b89ed6d9310d3a9d222025-01-22T01:21:08ZengUniversity of BaghdadIbn Al-Haitham Journal for Pure and Applied Sciences1609-40422521-34072025-01-0138110.30526/38.1.3515Oscillation Criteria for Solutions of Neutral Differential Equations of the Second-Order Emden-Fowler Type with Forcing Term Jihan Saad0https://orcid.org/0009-0000-2264-7057Hussain Ali Mohamad1https://orcid.org/0000-0002-4684-786XDepartment of Mathematics, College of Science for Women, University of Baghdad, Baghdad, Iraq. Department of Mathematics, College of Science for Women, University of Baghdad, Baghdad, Iraq. In this paper, the oscillation property and the asymptotic behavior of solutions of neutral second-order differential Equations of the Emden-Fowler type were studied under the influence of the coefficients of forces. It has been shown through this research that the coefficients of forces in addition to the Emden-Fowler type have a major role on the oscillation of solutions of neutral Equations. As well as its effect on the convergence and divergence of nonoscillatory solutions. For this purpose, some conditions are obtained to ensure that all solutions of the neutral Equations Emden-Fowler type oscillating or nonoscillating go to ∞, as t → ∞. Some of these conditions are the development of conditions similar to them in some of the well-known results included in the references, for example, condition (8) in this research with condition (4) in (9). The obtained results included some illustrative examples showing that the resulting conditions are easy to apply and guarantee oscillation. https://jih.uobaghdad.edu.iq/index.php/j/article/view/3515Oscillation, Asymptotic behavior, Emden-Fowler, Forcing Term. |
| spellingShingle | Jihan Saad Hussain Ali Mohamad Oscillation Criteria for Solutions of Neutral Differential Equations of the Second-Order Emden-Fowler Type with Forcing Term Ibn Al-Haitham Journal for Pure and Applied Sciences Oscillation, Asymptotic behavior, Emden-Fowler, Forcing Term. |
| title | Oscillation Criteria for Solutions of Neutral Differential Equations of the Second-Order Emden-Fowler Type with Forcing Term |
| title_full | Oscillation Criteria for Solutions of Neutral Differential Equations of the Second-Order Emden-Fowler Type with Forcing Term |
| title_fullStr | Oscillation Criteria for Solutions of Neutral Differential Equations of the Second-Order Emden-Fowler Type with Forcing Term |
| title_full_unstemmed | Oscillation Criteria for Solutions of Neutral Differential Equations of the Second-Order Emden-Fowler Type with Forcing Term |
| title_short | Oscillation Criteria for Solutions of Neutral Differential Equations of the Second-Order Emden-Fowler Type with Forcing Term |
| title_sort | oscillation criteria for solutions of neutral differential equations of the second order emden fowler type with forcing term |
| topic | Oscillation, Asymptotic behavior, Emden-Fowler, Forcing Term. |
| url | https://jih.uobaghdad.edu.iq/index.php/j/article/view/3515 |
| work_keys_str_mv | AT jihansaad oscillationcriteriaforsolutionsofneutraldifferentialequationsofthesecondorderemdenfowlertypewithforcingterm AT hussainalimohamad oscillationcriteriaforsolutionsofneutraldifferentialequationsofthesecondorderemdenfowlertypewithforcingterm |