Oscillation of Second-Order Neutral Functional Differential Equations with Mixed Nonlinearities
We study the following second-order neutral functional differential equation with mixed nonlinearities (r(t)|(u(t)+p(t)u(t-σ))'|α-1(u(t)+p(t)u(t-σ))′)′+q0(t)|u(τ0(t))|α-1u(τ0(t))+q1(t)|u(τ1(t))|β-1u(τ1(t))+q2(t)|u(τ2(t))|γ-1u(τ2(t))=0, where γ>α>β>0, ∫t0∞(1/r1/α(t))dt<∞. Oscillation...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/927690 |
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| author | Shurong Sun Tongxing Li Zhenlai Han Yibing Sun |
| author_facet | Shurong Sun Tongxing Li Zhenlai Han Yibing Sun |
| author_sort | Shurong Sun |
| collection | DOAJ |
| description | We study the following second-order neutral functional differential equation with mixed nonlinearities (r(t)|(u(t)+p(t)u(t-σ))'|α-1(u(t)+p(t)u(t-σ))′)′+q0(t)|u(τ0(t))|α-1u(τ0(t))+q1(t)|u(τ1(t))|β-1u(τ1(t))+q2(t)|u(τ2(t))|γ-1u(τ2(t))=0, where γ>α>β>0, ∫t0∞(1/r1/α(t))dt<∞. Oscillation results for the equation are established which improve the results obtained by Sun and Meng (2006), Xu and Meng (2006), Sun and Meng (2009), and Han et al. (2010). |
| format | Article |
| id | doaj-art-8abb2af1c1434241b3d7c546a95690ec |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-8abb2af1c1434241b3d7c546a95690ec2025-02-03T01:12:58ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/927690927690Oscillation of Second-Order Neutral Functional Differential Equations with Mixed NonlinearitiesShurong Sun0Tongxing Li1Zhenlai Han2Yibing Sun3School of Science, University of Jinan, Jinan, Shandong 250022, ChinaSchool of Science, University of Jinan, Jinan, Shandong 250022, ChinaSchool of Science, University of Jinan, Jinan, Shandong 250022, ChinaSchool of Science, University of Jinan, Jinan, Shandong 250022, ChinaWe study the following second-order neutral functional differential equation with mixed nonlinearities (r(t)|(u(t)+p(t)u(t-σ))'|α-1(u(t)+p(t)u(t-σ))′)′+q0(t)|u(τ0(t))|α-1u(τ0(t))+q1(t)|u(τ1(t))|β-1u(τ1(t))+q2(t)|u(τ2(t))|γ-1u(τ2(t))=0, where γ>α>β>0, ∫t0∞(1/r1/α(t))dt<∞. Oscillation results for the equation are established which improve the results obtained by Sun and Meng (2006), Xu and Meng (2006), Sun and Meng (2009), and Han et al. (2010).http://dx.doi.org/10.1155/2011/927690 |
| spellingShingle | Shurong Sun Tongxing Li Zhenlai Han Yibing Sun Oscillation of Second-Order Neutral Functional Differential Equations with Mixed Nonlinearities Abstract and Applied Analysis |
| title | Oscillation of Second-Order Neutral Functional Differential Equations with Mixed Nonlinearities |
| title_full | Oscillation of Second-Order Neutral Functional Differential Equations with Mixed Nonlinearities |
| title_fullStr | Oscillation of Second-Order Neutral Functional Differential Equations with Mixed Nonlinearities |
| title_full_unstemmed | Oscillation of Second-Order Neutral Functional Differential Equations with Mixed Nonlinearities |
| title_short | Oscillation of Second-Order Neutral Functional Differential Equations with Mixed Nonlinearities |
| title_sort | oscillation of second order neutral functional differential equations with mixed nonlinearities |
| url | http://dx.doi.org/10.1155/2011/927690 |
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