Interval Oscillation Criteria of Second Order Mixed Nonlinear Impulsive Differential Equations with Delay

Zhonghai Guo, Xiaoliang Zhou and Wu-Sheng Wang

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: 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.

Date: 2012
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https://doi.org/10.1155/2012/351709

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:351709

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