Interval Oscillation Criteria of Second Order Mixed Nonlinear Impulsive Differential Equations with Delay
We study the following second order mixed nonlinear impulsive differential equations with delay (r(t)Φα(x′(t)))′+p0(t)Φα(x(t))+∑i=1npi(t)Φβi(x(t-σ))=e(t), t≥t0, t≠τk,x(τk+)=akx(τk), x'(τk+)=bkx'(τk), k=1,2,…, where Φ*(u)=|u|*-1u, σ is a nonnegative constant, {τk} denotes the impulsive mome...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/351709 |
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| author | Zhonghai Guo Xiaoliang Zhou Wu-Sheng Wang |
| author_facet | Zhonghai Guo Xiaoliang Zhou Wu-Sheng Wang |
| author_sort | Zhonghai Guo |
| collection | DOAJ |
| description | We study the following second order mixed nonlinear impulsive differential equations with delay (r(t)Φα(x′(t)))′+p0(t)Φα(x(t))+∑i=1npi(t)Φβi(x(t-σ))=e(t), t≥t0, t≠τk,x(τk+)=akx(τk), x'(τk+)=bkx'(τk), k=1,2,…, where Φ*(u)=|u|*-1u, σ is a nonnegative constant, {τk} denotes the impulsive moments sequence, and τk+1-τk>σ. Some sufficient conditions for the interval oscillation criteria of the equations are obtained. The results obtained generalize and improve earlier ones. Two examples are considered to illustrate the main results. |
| format | Article |
| id | doaj-art-12d1bbbcba6b4271b9916f5607b2d5dd |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-12d1bbbcba6b4271b9916f5607b2d5dd2025-08-20T03:55:44ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/351709351709Interval Oscillation Criteria of Second Order Mixed Nonlinear Impulsive Differential Equations with DelayZhonghai Guo0Xiaoliang Zhou1Wu-Sheng Wang2Department of Mathematics, Xinzhou Teachers University, Shanxi, Xinzhou 034000, ChinaDepartment of Mathematics, Guangdong Ocean University, Guangdong, Zhanjiang 524088, ChinaDepartment of Mathematics, Hechi University, Guangxi, Yizhou 546300, ChinaWe study the following second order mixed nonlinear impulsive differential equations with delay (r(t)Φα(x′(t)))′+p0(t)Φα(x(t))+∑i=1npi(t)Φβi(x(t-σ))=e(t), t≥t0, t≠τk,x(τk+)=akx(τk), x'(τk+)=bkx'(τk), k=1,2,…, where Φ*(u)=|u|*-1u, σ is a nonnegative constant, {τk} denotes the impulsive moments sequence, and τk+1-τk>σ. Some sufficient conditions for the interval oscillation criteria of the equations are obtained. The results obtained generalize and improve earlier ones. Two examples are considered to illustrate the main results.http://dx.doi.org/10.1155/2012/351709 |
| spellingShingle | Zhonghai Guo Xiaoliang Zhou Wu-Sheng Wang Interval Oscillation Criteria of Second Order Mixed Nonlinear Impulsive Differential Equations with Delay Abstract and Applied Analysis |
| title | Interval Oscillation Criteria of Second Order Mixed Nonlinear Impulsive Differential Equations with Delay |
| title_full | Interval Oscillation Criteria of Second Order Mixed Nonlinear Impulsive Differential Equations with Delay |
| title_fullStr | Interval Oscillation Criteria of Second Order Mixed Nonlinear Impulsive Differential Equations with Delay |
| title_full_unstemmed | Interval Oscillation Criteria of Second Order Mixed Nonlinear Impulsive Differential Equations with Delay |
| title_short | Interval Oscillation Criteria of Second Order Mixed Nonlinear Impulsive Differential Equations with Delay |
| title_sort | interval oscillation criteria of second order mixed nonlinear impulsive differential equations with delay |
| url | http://dx.doi.org/10.1155/2012/351709 |
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