Oscillation Theorems for Second-Order Half-Linear Advanced Dynamic Equations on Time Scales
This paper is concerned with the oscillatory behavior of the second-order half-linear advanced dynamic equation (𝑟(𝑡)(𝑥Δ(𝑡))𝛾)Δ+𝑝(𝑡)𝑥𝛾(𝑔(𝑡))=0 on an arbitrary time scale 𝕋 with sup 𝕋=∞, where 𝑔(𝑡)≥𝑡 and ∫∞𝑡𝑜(Δ𝑠/(𝑟1/𝛾(𝑠)))<∞. Some sufficient conditions for oscillation of the studied equation are e...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2011/840569 |
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| author | Shuhong Tang Tongxing Li Ethiraju Thandapani |
| author_facet | Shuhong Tang Tongxing Li Ethiraju Thandapani |
| author_sort | Shuhong Tang |
| collection | DOAJ |
| description | This paper is concerned with the oscillatory behavior of the second-order half-linear advanced dynamic equation
(𝑟(𝑡)(𝑥Δ(𝑡))𝛾)Δ+𝑝(𝑡)𝑥𝛾(𝑔(𝑡))=0 on an arbitrary time scale 𝕋 with sup 𝕋=∞, where 𝑔(𝑡)≥𝑡 and ∫∞𝑡𝑜(Δ𝑠/(𝑟1/𝛾(𝑠)))<∞. Some sufficient conditions for oscillation of the studied equation are established. Our results not only improve and complement those results in the literature but also unify the oscillation of the second-order half-linear advanced differential equation and the second-order half-linear advanced difference equation. Three examples are included to illustrate the main results. |
| format | Article |
| id | doaj-art-865d80a3df0146c3862c03c6f13eeb30 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-865d80a3df0146c3862c03c6f13eeb302025-02-03T06:13:43ZengWileyInternational Journal of Differential Equations1687-96431687-96512011-01-01201110.1155/2011/840569840569Oscillation Theorems for Second-Order Half-Linear Advanced Dynamic Equations on Time ScalesShuhong Tang0Tongxing Li1Ethiraju Thandapani2School of Information and Control Engineering, Weifang University, Shandong, Weifang 261061, ChinaSchool of Control Science and Engineering, Shandong University, Shandong, Jinan 250061, ChinaRamanujan Institute for Advanced Study in Mathematics, University of Madras, 600 005 Chennai, IndiaThis paper is concerned with the oscillatory behavior of the second-order half-linear advanced dynamic equation (𝑟(𝑡)(𝑥Δ(𝑡))𝛾)Δ+𝑝(𝑡)𝑥𝛾(𝑔(𝑡))=0 on an arbitrary time scale 𝕋 with sup 𝕋=∞, where 𝑔(𝑡)≥𝑡 and ∫∞𝑡𝑜(Δ𝑠/(𝑟1/𝛾(𝑠)))<∞. Some sufficient conditions for oscillation of the studied equation are established. Our results not only improve and complement those results in the literature but also unify the oscillation of the second-order half-linear advanced differential equation and the second-order half-linear advanced difference equation. Three examples are included to illustrate the main results.http://dx.doi.org/10.1155/2011/840569 |
| spellingShingle | Shuhong Tang Tongxing Li Ethiraju Thandapani Oscillation Theorems for Second-Order Half-Linear Advanced Dynamic Equations on Time Scales International Journal of Differential Equations |
| title | Oscillation Theorems for Second-Order Half-Linear Advanced Dynamic Equations on Time Scales |
| title_full | Oscillation Theorems for Second-Order Half-Linear Advanced Dynamic Equations on Time Scales |
| title_fullStr | Oscillation Theorems for Second-Order Half-Linear Advanced Dynamic Equations on Time Scales |
| title_full_unstemmed | Oscillation Theorems for Second-Order Half-Linear Advanced Dynamic Equations on Time Scales |
| title_short | Oscillation Theorems for Second-Order Half-Linear Advanced Dynamic Equations on Time Scales |
| title_sort | oscillation theorems for second order half linear advanced dynamic equations on time scales |
| url | http://dx.doi.org/10.1155/2011/840569 |
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