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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |