Abstract and Applied Analysis
Volume 2011 (2011), Article ID 458275, 11 pages
http://dx.doi.org/10.1155/2011/458275
Research Article

Oscillation of Second-Order Sublinear Impulsive Differential Equations

A. Zafer

Department of Mathematics, Middle East Technical University, 06800 Ankara, Turkey

Received 25 January 2011; Accepted 27 February 2011

Academic Editor: Josef Diblík

Copyright © 2011 A. Zafer. 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

Oscillation criteria obtained by Kusano and Onose (1973) and by Belohorec (1969) are extended to second-order sublinear impulsive differential equations of Emden-Fowler type: 𝑥 ′ ′ ( 𝑡 ) + 𝑝 ( 𝑡 ) | 𝑥 ( 𝜏 ( 𝑡 ) ) | 𝛼 − 1 𝑥 ( 𝜏 ( 𝑡 ) ) = 0 , 𝑡 ≠ 𝜃 𝑘 ; Δ 𝑥 ′ ( 𝑡 ) | 𝑡 = 𝜃 𝑘 + 𝑞 𝑘 | 𝑥 ( 𝜏 ( 𝜃 𝑘 ) ) | 𝛼 − 1 𝑥 ( 𝜏 ( 𝜃 𝑘 ) ) = 0 ; Δ 𝑥 ( 𝑡 ) | 𝑡 = 𝜃 𝑘 = 0 , ( 0 < 𝛼 < 1 ) by considering the cases 𝜏 ( 𝑡 ) ≤ 𝑡 and 𝜏 ( 𝑡 ) = 𝑡 , respectively. Examples are inserted to show how impulsive perturbations greatly affect the oscillation behavior of the solutions.