Forced Oscillation of Second-Order Half-Linear Dynamic Equations on Time Scales
We will establish a new interval oscillation criterion for second-order half-linear dynamic equation (r(t)[xΔ(t)]α)Δ+p(t)xα(σ(t))=f(t) on a time scale T which is unbounded, which is a extension of the oscillation result for second order linear dynamic equation established by Erbe et al. (2008). As a...
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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/10.1155/2010/294194 |
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| _version_ | 1832556960057131008 |
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| author | Quanwen Lin Baoguo Jia Qiru Wang |
| author_facet | Quanwen Lin Baoguo Jia Qiru Wang |
| author_sort | Quanwen Lin |
| collection | DOAJ |
| description | We will establish a new interval oscillation criterion for second-order half-linear dynamic equation (r(t)[xΔ(t)]α)Δ+p(t)xα(σ(t))=f(t) on a time scale T which is unbounded, which is a extension of the oscillation result for second order linear dynamic equation established by Erbe et al. (2008). As an application, we obtain a sufficient condition of oscillation of the second-order half-linear differential equation ([x′(t)]α)′+csintxα(t)=cost, where α=p/q, p, q are odd positive integers. |
| format | Article |
| id | doaj-art-7d80520eb67544ba9367384bcf3841b6 |
| 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-7d80520eb67544ba9367384bcf3841b62025-02-03T05:43:59ZengWileyAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/294194294194Forced Oscillation of Second-Order Half-Linear Dynamic Equations on Time ScalesQuanwen Lin0Baoguo Jia1Qiru Wang2Department of Mathematics, Maoming University, Maoming 525000, ChinaDepartment of Mathematics, Sun Yat-sen University, Guangzhou 510275, ChinaDepartment of Mathematics, Sun Yat-sen University, Guangzhou 510275, ChinaWe will establish a new interval oscillation criterion for second-order half-linear dynamic equation (r(t)[xΔ(t)]α)Δ+p(t)xα(σ(t))=f(t) on a time scale T which is unbounded, which is a extension of the oscillation result for second order linear dynamic equation established by Erbe et al. (2008). As an application, we obtain a sufficient condition of oscillation of the second-order half-linear differential equation ([x′(t)]α)′+csintxα(t)=cost, where α=p/q, p, q are odd positive integers.http://dx.doi.org/10.1155/2010/294194 |
| spellingShingle | Quanwen Lin Baoguo Jia Qiru Wang Forced Oscillation of Second-Order Half-Linear Dynamic Equations on Time Scales Abstract and Applied Analysis |
| title | Forced Oscillation of Second-Order Half-Linear Dynamic Equations on Time Scales |
| title_full | Forced Oscillation of Second-Order Half-Linear Dynamic Equations on Time Scales |
| title_fullStr | Forced Oscillation of Second-Order Half-Linear Dynamic Equations on Time Scales |
| title_full_unstemmed | Forced Oscillation of Second-Order Half-Linear Dynamic Equations on Time Scales |
| title_short | Forced Oscillation of Second-Order Half-Linear Dynamic Equations on Time Scales |
| title_sort | forced oscillation of second order half linear dynamic equations on time scales |
| url | http://dx.doi.org/10.1155/2010/294194 |
| work_keys_str_mv | AT quanwenlin forcedoscillationofsecondorderhalflineardynamicequationsontimescales AT baoguojia forcedoscillationofsecondorderhalflineardynamicequationsontimescales AT qiruwang forcedoscillationofsecondorderhalflineardynamicequationsontimescales |