Oscillation Criteria for Second-Order Superlinear Neutral Differential Equations
Some oscillation criteria are established for the second-order superlinear neutral differential equations (r(t)|z'(t)|α-1z'(t))'+f(t,x(σ(t)))=0, t≥t0, where z(t)=x(t)+p(t)x(τ(t)), τ(t)≥t, σ(t)≥t, p∈C([t0,∞),[0,p0]), and α≥1. Our results are based on the cases ∫t0∞1/r1/α(t)dt=∞ or ∫t0∞...
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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/10.1155/2011/367541 |
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| author | Tongxing Li Zhenlai Han Chenghui Zhang Hua Li |
| author_facet | Tongxing Li Zhenlai Han Chenghui Zhang Hua Li |
| author_sort | Tongxing Li |
| collection | DOAJ |
| description | Some oscillation criteria are established for the second-order superlinear neutral differential equations (r(t)|z'(t)|α-1z'(t))'+f(t,x(σ(t)))=0, t≥t0, where z(t)=x(t)+p(t)x(τ(t)), τ(t)≥t, σ(t)≥t, p∈C([t0,∞),[0,p0]), and α≥1. Our results are based on the cases ∫t0∞1/r1/α(t)dt=∞ or ∫t0∞1/r1/α(t)dt<∞. Two examples are also provided to illustrate these results. |
| format | Article |
| id | doaj-art-2c32d71542574c2e8d195b28d8d770df |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-2c32d71542574c2e8d195b28d8d770df2025-08-20T02:07:38ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/367541367541Oscillation Criteria for Second-Order Superlinear Neutral Differential EquationsTongxing Li0Zhenlai Han1Chenghui Zhang2Hua Li3School of Science, University of Jinan, Jinan, Shandong 250022, ChinaSchool of Science, University of Jinan, Jinan, Shandong 250022, ChinaSchool of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, ChinaSchool of Science, University of Jinan, Jinan, Shandong 250022, ChinaSome oscillation criteria are established for the second-order superlinear neutral differential equations (r(t)|z'(t)|α-1z'(t))'+f(t,x(σ(t)))=0, t≥t0, where z(t)=x(t)+p(t)x(τ(t)), τ(t)≥t, σ(t)≥t, p∈C([t0,∞),[0,p0]), and α≥1. Our results are based on the cases ∫t0∞1/r1/α(t)dt=∞ or ∫t0∞1/r1/α(t)dt<∞. Two examples are also provided to illustrate these results.http://dx.doi.org/10.1155/2011/367541 |
| spellingShingle | Tongxing Li Zhenlai Han Chenghui Zhang Hua Li Oscillation Criteria for Second-Order Superlinear Neutral Differential Equations Abstract and Applied Analysis |
| title | Oscillation Criteria for Second-Order Superlinear Neutral Differential Equations |
| title_full | Oscillation Criteria for Second-Order Superlinear Neutral Differential Equations |
| title_fullStr | Oscillation Criteria for Second-Order Superlinear Neutral Differential Equations |
| title_full_unstemmed | Oscillation Criteria for Second-Order Superlinear Neutral Differential Equations |
| title_short | Oscillation Criteria for Second-Order Superlinear Neutral Differential Equations |
| title_sort | oscillation criteria for second order superlinear neutral differential equations |
| url | http://dx.doi.org/10.1155/2011/367541 |
| work_keys_str_mv | AT tongxingli oscillationcriteriaforsecondordersuperlinearneutraldifferentialequations AT zhenlaihan oscillationcriteriaforsecondordersuperlinearneutraldifferentialequations AT chenghuizhang oscillationcriteriaforsecondordersuperlinearneutraldifferentialequations AT huali oscillationcriteriaforsecondordersuperlinearneutraldifferentialequations |