Oscillation of higher-order differential equations with distributed delay
Abstract This paper deals with the oscillation properties of higher-order nonlinear differential equations with distributed delay [b(ℓ)(y(n−1)(ℓ))γ]′+∫cdq(ℓ,ξ)yγ(g(ℓ,ξ))d(ξ)=0,ℓ≥ℓ0, $$ \bigl[ b ( \ell ) \bigl( y^{ ( n-1 ) } ( \ell ) \bigr) ^{\gamma} \bigr] ^{\prime}+ \int_{c}^{d}q ( \ell, \xi ) y^{\...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-03-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-019-2003-0 |
| _version_ | 1819131329794539520 |
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| author | O. Bazighifan E. M. Elabbasy O. Moaaz |
| author_facet | O. Bazighifan E. M. Elabbasy O. Moaaz |
| author_sort | O. Bazighifan |
| collection | DOAJ |
| description | Abstract This paper deals with the oscillation properties of higher-order nonlinear differential equations with distributed delay [b(ℓ)(y(n−1)(ℓ))γ]′+∫cdq(ℓ,ξ)yγ(g(ℓ,ξ))d(ξ)=0,ℓ≥ℓ0, $$ \bigl[ b ( \ell ) \bigl( y^{ ( n-1 ) } ( \ell ) \bigr) ^{\gamma} \bigr] ^{\prime}+ \int_{c}^{d}q ( \ell, \xi ) y^{\gamma} \bigl( g ( \ell, \xi ) \bigr) \,d ( \xi ) =0, \quad \ell\geq\ell_{0}, $$ under the condition ∫ℓ0∞1b1γ(ℓ)dℓ<∞. $$ \int_{\ell_{0}}^{\infty}\frac{1}{b^{\frac{1}{\gamma}} ( \ell ) }\,d\ell< \infty. $$ We obtain new oscillation criteria by employing a refinement of the generalized Riccati transformations and new comparison principles. We provide some examples to illustrate the main results. |
| first_indexed | 2024-12-22T09:13:47Z |
| format | Article |
| id | doaj.art-0eee2bf568664473b111eb175963dc7d |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-22T09:13:47Z |
| publishDate | 2019-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-0eee2bf568664473b111eb175963dc7d2022-12-21T18:31:21ZengSpringerOpenJournal of Inequalities and Applications1029-242X2019-03-01201911910.1186/s13660-019-2003-0Oscillation of higher-order differential equations with distributed delayO. Bazighifan0E. M. Elabbasy1O. Moaaz2Department of Mathematics, Faculty of Education, Hadhramout UniversityDepartment of Mathematics, Faculty of Science, Mansoura UniversityDepartment of Mathematics, Faculty of Science, Mansoura UniversityAbstract This paper deals with the oscillation properties of higher-order nonlinear differential equations with distributed delay [b(ℓ)(y(n−1)(ℓ))γ]′+∫cdq(ℓ,ξ)yγ(g(ℓ,ξ))d(ξ)=0,ℓ≥ℓ0, $$ \bigl[ b ( \ell ) \bigl( y^{ ( n-1 ) } ( \ell ) \bigr) ^{\gamma} \bigr] ^{\prime}+ \int_{c}^{d}q ( \ell, \xi ) y^{\gamma} \bigl( g ( \ell, \xi ) \bigr) \,d ( \xi ) =0, \quad \ell\geq\ell_{0}, $$ under the condition ∫ℓ0∞1b1γ(ℓ)dℓ<∞. $$ \int_{\ell_{0}}^{\infty}\frac{1}{b^{\frac{1}{\gamma}} ( \ell ) }\,d\ell< \infty. $$ We obtain new oscillation criteria by employing a refinement of the generalized Riccati transformations and new comparison principles. We provide some examples to illustrate the main results.http://link.springer.com/article/10.1186/s13660-019-2003-0Higher-orderDistributed delay differential equationsOscillatory solutionsNonoscillatory solutions |
| spellingShingle | O. Bazighifan E. M. Elabbasy O. Moaaz Oscillation of higher-order differential equations with distributed delay Journal of Inequalities and Applications Higher-order Distributed delay differential equations Oscillatory solutions Nonoscillatory solutions |
| title | Oscillation of higher-order differential equations with distributed delay |
| title_full | Oscillation of higher-order differential equations with distributed delay |
| title_fullStr | Oscillation of higher-order differential equations with distributed delay |
| title_full_unstemmed | Oscillation of higher-order differential equations with distributed delay |
| title_short | Oscillation of higher-order differential equations with distributed delay |
| title_sort | oscillation of higher order differential equations with distributed delay |
| topic | Higher-order Distributed delay differential equations Oscillatory solutions Nonoscillatory solutions |
| url | http://link.springer.com/article/10.1186/s13660-019-2003-0 |
| work_keys_str_mv | AT obazighifan oscillationofhigherorderdifferentialequationswithdistributeddelay AT emelabbasy oscillationofhigherorderdifferentialequationswithdistributeddelay AT omoaaz oscillationofhigherorderdifferentialequationswithdistributeddelay |