New Oscillation Criteria for Second-Order Neutral Delay Differential Equations with Positive and Negative Coefficients
We establish the oscillation and asymptotic criteria for the second-order neutral delay differential equations with positive and negative coefficients having the forms [x(t)+∑i∈Rci(t)x(αi(t))]′′+r(t)[x(t)+∑i∈Rci(t)x(αi(t))]′+∑i∈Ppi(t)x(βi(t))-∑i∈Qqi(t)x(γi(t))=0 and [x(t)+∑i∈Rci(t)x(αi(t))]′′+r(t)[x...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/564068 |
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| author | Yuzhen Bai Lihua Liu |
| author_facet | Yuzhen Bai Lihua Liu |
| author_sort | Yuzhen Bai |
| collection | DOAJ |
| description | We establish the oscillation and asymptotic criteria for the second-order neutral delay differential equations with positive and negative coefficients having the forms [x(t)+∑i∈Rci(t)x(αi(t))]′′+r(t)[x(t)+∑i∈Rci(t)x(αi(t))]′+∑i∈Ppi(t)x(βi(t))-∑i∈Qqi(t)x(γi(t))=0 and [x(t)+∑i∈Rci(t)x(αi(t))]′′+r(t)[x(t)+∑i∈Rci(t)x(αi(t))]′+∑i∈Ppi(t)x(βi(t))-∑i∈Qqi(t)x(γi(t))=f(t). The obtained new oscillation criteria extend and improve the recent results given in the paperof B. Karpuz et al. (2009). |
| format | Article |
| id | doaj-art-d734a483069b461794ecb7546983bde3 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d734a483069b461794ecb7546983bde32025-02-03T01:28:37ZengWileyAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/564068564068New Oscillation Criteria for Second-Order Neutral Delay Differential Equations with Positive and Negative CoefficientsYuzhen Bai0Lihua Liu1School of Mathematical Sciences, Qufu Normal University, Qufu 273165, ChinaSchool of Mathematical Sciences, Qufu Normal University, Qufu 273165, ChinaWe establish the oscillation and asymptotic criteria for the second-order neutral delay differential equations with positive and negative coefficients having the forms [x(t)+∑i∈Rci(t)x(αi(t))]′′+r(t)[x(t)+∑i∈Rci(t)x(αi(t))]′+∑i∈Ppi(t)x(βi(t))-∑i∈Qqi(t)x(γi(t))=0 and [x(t)+∑i∈Rci(t)x(αi(t))]′′+r(t)[x(t)+∑i∈Rci(t)x(αi(t))]′+∑i∈Ppi(t)x(βi(t))-∑i∈Qqi(t)x(γi(t))=f(t). The obtained new oscillation criteria extend and improve the recent results given in the paperof B. Karpuz et al. (2009).http://dx.doi.org/10.1155/2010/564068 |
| spellingShingle | Yuzhen Bai Lihua Liu New Oscillation Criteria for Second-Order Neutral Delay Differential Equations with Positive and Negative Coefficients Abstract and Applied Analysis |
| title | New Oscillation Criteria for Second-Order Neutral Delay Differential Equations with Positive and Negative Coefficients |
| title_full | New Oscillation Criteria for Second-Order Neutral Delay Differential Equations with Positive and Negative Coefficients |
| title_fullStr | New Oscillation Criteria for Second-Order Neutral Delay Differential Equations with Positive and Negative Coefficients |
| title_full_unstemmed | New Oscillation Criteria for Second-Order Neutral Delay Differential Equations with Positive and Negative Coefficients |
| title_short | New Oscillation Criteria for Second-Order Neutral Delay Differential Equations with Positive and Negative Coefficients |
| title_sort | new oscillation criteria for second order neutral delay differential equations with positive and negative coefficients |
| url | http://dx.doi.org/10.1155/2010/564068 |
| work_keys_str_mv | AT yuzhenbai newoscillationcriteriaforsecondorderneutraldelaydifferentialequationswithpositiveandnegativecoefficients AT lihualiu newoscillationcriteriaforsecondorderneutraldelaydifferentialequationswithpositiveandnegativecoefficients |