Interval Oscillation Criteria for Second-Order Nonlinear Forced Dynamic Equations with Damping on Time Scales
By using the Riccati transformation technique and constructing a class of Philos-type functions on time scales, we establish some new interval oscillation criteria for the second-order damped nonlinear dynamic equations with forced term of the form (r(t)xΔ(t))Δ+p(t)xΔσ(t)+q(t)(xσ(t))α=F(t,xσ(t)) on...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/359240 |
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| _version_ | 1850230547394068480 |
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| author | Yibing Sun Zhenlai Han Shurong Sun Chao Zhang |
| author_facet | Yibing Sun Zhenlai Han Shurong Sun Chao Zhang |
| author_sort | Yibing Sun |
| collection | DOAJ |
| description | By using the Riccati transformation technique and constructing a class of Philos-type functions on time scales, we establish some new interval oscillation criteria for the second-order damped nonlinear dynamic equations with forced term of the form (r(t)xΔ(t))Δ+p(t)xΔσ(t)+q(t)(xσ(t))α=F(t,xσ(t)) on a time scale 𝕋 which is unbounded, where α is a quotient of odd positive integer. Our results in this paper extend and improve some known results. Some examples are given here to illustrate our main results. |
| format | Article |
| id | doaj-art-2911a9f8ebda48d7b7063774a0240f5d |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-2911a9f8ebda48d7b7063774a0240f5d2025-08-20T02:03:51ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/359240359240Interval Oscillation Criteria for Second-Order Nonlinear Forced Dynamic Equations with Damping on Time ScalesYibing Sun0Zhenlai Han1Shurong Sun2Chao Zhang3School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, ChinaSchool of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, ChinaSchool of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, ChinaSchool of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, ChinaBy using the Riccati transformation technique and constructing a class of Philos-type functions on time scales, we establish some new interval oscillation criteria for the second-order damped nonlinear dynamic equations with forced term of the form (r(t)xΔ(t))Δ+p(t)xΔσ(t)+q(t)(xσ(t))α=F(t,xσ(t)) on a time scale 𝕋 which is unbounded, where α is a quotient of odd positive integer. Our results in this paper extend and improve some known results. Some examples are given here to illustrate our main results.http://dx.doi.org/10.1155/2013/359240 |
| spellingShingle | Yibing Sun Zhenlai Han Shurong Sun Chao Zhang Interval Oscillation Criteria for Second-Order Nonlinear Forced Dynamic Equations with Damping on Time Scales Abstract and Applied Analysis |
| title | Interval Oscillation Criteria for Second-Order Nonlinear Forced Dynamic Equations with Damping on Time Scales |
| title_full | Interval Oscillation Criteria for Second-Order Nonlinear Forced Dynamic Equations with Damping on Time Scales |
| title_fullStr | Interval Oscillation Criteria for Second-Order Nonlinear Forced Dynamic Equations with Damping on Time Scales |
| title_full_unstemmed | Interval Oscillation Criteria for Second-Order Nonlinear Forced Dynamic Equations with Damping on Time Scales |
| title_short | Interval Oscillation Criteria for Second-Order Nonlinear Forced Dynamic Equations with Damping on Time Scales |
| title_sort | interval oscillation criteria for second order nonlinear forced dynamic equations with damping on time scales |
| url | http://dx.doi.org/10.1155/2013/359240 |
| work_keys_str_mv | AT yibingsun intervaloscillationcriteriaforsecondordernonlinearforceddynamicequationswithdampingontimescales AT zhenlaihan intervaloscillationcriteriaforsecondordernonlinearforceddynamicequationswithdampingontimescales AT shurongsun intervaloscillationcriteriaforsecondordernonlinearforceddynamicequationswithdampingontimescales AT chaozhang intervaloscillationcriteriaforsecondordernonlinearforceddynamicequationswithdampingontimescales |