New Oscillation Criteria for Second-Order Delay Differential Equations with Mixed Nonlinearities
We establish new oscillation criteria for second-order delay differential equations with mixed nonlinearities of the form (p(t)x'(t))'+∑i=1npi(t)x(t-τi)+∑i=1nqi(t)|x(t-τi)|αisgn x(t-τi)=e(t), t≥0, where p(t), pi(t), qi(t), and e(t) are continuous functions defined on [0,∞), and p(t)>0,...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2010/796256 |
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| author | Yuzhen Bai Lihua Liu |
| author_facet | Yuzhen Bai Lihua Liu |
| author_sort | Yuzhen Bai |
| collection | DOAJ |
| description | We establish new oscillation criteria for second-order delay differential equations with mixed nonlinearities of the form (p(t)x'(t))'+∑i=1npi(t)x(t-τi)+∑i=1nqi(t)|x(t-τi)|αisgn x(t-τi)=e(t), t≥0, where p(t), pi(t), qi(t), and e(t) are continuous functions defined on [0,∞), and p(t)>0, p′(t)≥0, and α1>⋯>αm>1>αm+1>⋯>αn>0. No restriction is imposed on the potentials pi(t), qi(t), and e(t) to be nonnegative. These oscillation criteria extend and improve the results given in the recent papers. An interesting example illustrating the sharpness of our results is also provided. |
| format | Article |
| id | doaj-art-d26502b1eebd495a9aaaed69dcd15b6f |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-d26502b1eebd495a9aaaed69dcd15b6f2025-08-20T02:19:43ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2010-01-01201010.1155/2010/796256796256New Oscillation Criteria for Second-Order Delay Differential Equations with Mixed NonlinearitiesYuzhen Bai0Lihua Liu1School of Mathematical Sciences, Qufu Normal University, Qufu 273165, ChinaSchool of Mathematical Sciences, Qufu Normal University, Qufu 273165, ChinaWe establish new oscillation criteria for second-order delay differential equations with mixed nonlinearities of the form (p(t)x'(t))'+∑i=1npi(t)x(t-τi)+∑i=1nqi(t)|x(t-τi)|αisgn x(t-τi)=e(t), t≥0, where p(t), pi(t), qi(t), and e(t) are continuous functions defined on [0,∞), and p(t)>0, p′(t)≥0, and α1>⋯>αm>1>αm+1>⋯>αn>0. No restriction is imposed on the potentials pi(t), qi(t), and e(t) to be nonnegative. These oscillation criteria extend and improve the results given in the recent papers. An interesting example illustrating the sharpness of our results is also provided.http://dx.doi.org/10.1155/2010/796256 |
| spellingShingle | Yuzhen Bai Lihua Liu New Oscillation Criteria for Second-Order Delay Differential Equations with Mixed Nonlinearities Discrete Dynamics in Nature and Society |
| title | New Oscillation Criteria for Second-Order Delay Differential Equations with Mixed Nonlinearities |
| title_full | New Oscillation Criteria for Second-Order Delay Differential Equations with Mixed Nonlinearities |
| title_fullStr | New Oscillation Criteria for Second-Order Delay Differential Equations with Mixed Nonlinearities |
| title_full_unstemmed | New Oscillation Criteria for Second-Order Delay Differential Equations with Mixed Nonlinearities |
| title_short | New Oscillation Criteria for Second-Order Delay Differential Equations with Mixed Nonlinearities |
| title_sort | new oscillation criteria for second order delay differential equations with mixed nonlinearities |
| url | http://dx.doi.org/10.1155/2010/796256 |
| work_keys_str_mv | AT yuzhenbai newoscillationcriteriaforsecondorderdelaydifferentialequationswithmixednonlinearities AT lihualiu newoscillationcriteriaforsecondorderdelaydifferentialequationswithmixednonlinearities |