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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 285051, 22 pages
http://dx.doi.org/10.1155/2012/285051
Research Article

Interval Oscillation Criteria for Super-Half-Linear Impulsive Differential Equations with Delay

1Department of Mathematics, Xinzhou Teachers University, Shanxi Xinzhou 034000, China
2Department of Mathematics, Guangdong Ocean University, Guangdong Zhanjiang 524088, China
3Department of Mathematics, Hechi University, Guangxi Yizhou 546300, China

Received 25 April 2012; Accepted 2 July 2012

Academic Editor: Alfredo Bellen

Copyright © 2012 Zhonghai Guo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the following second-order super-half-linear impulsive differential equations with delay [r(t)φγ(x(t))]+p(t)φγ(x(t-σ))+q(t)f(x(t-σ))=e(t), tτk, x(t+)=akx(t), x(t+)=bkx(t), t=τk, where tt0, φ*(u)=|u|*-1u, σ is a nonnegative constant, {τk} denotes the impulsive moments sequence with τ1<τ2<<τk<, limkτk=, and τk+1-τk>σ. By some classical inequalities, Riccati transformation, and two classes of functions, we give several interval oscillation criteria which generalize and improve some known results. Moreover, we also give two examples to illustrate the effectiveness and nonemptiness of our results.