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Abstract and Applied Analysis
Volume 2011 (2011), Article ID 458275, 11 pages
Research Article

Oscillation of Second-Order Sublinear Impulsive Differential Equations

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

Received 25 January 2011; Accepted 27 February 2011

Academic Editor: Josef Diblรญk

Copyright ยฉ 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.


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: ๐‘ฅโ€ฒโ€ฒ(๐‘ก)+๐‘(๐‘ก)|๐‘ฅ(๐œ(๐‘ก))|๐›ผโˆ’1๐‘ฅ(๐œ(๐‘ก))=0, ๐‘กโ‰ ๐œƒ๐‘˜; ฮ”๐‘ฅโ€ฒ(๐‘ก)|๐‘ก=๐œƒ๐‘˜+๐‘ž๐‘˜|๐‘ฅ(๐œ(๐œƒ๐‘˜))|๐›ผโˆ’1๐‘ฅ(๐œ(๐œƒ๐‘˜))=0; ฮ”๐‘ฅ(๐‘ก)|๐‘ก=๐œƒ๐‘˜=0, (0<๐›ผ<1) by considering the cases ๐œ(๐‘ก)โ‰ค๐‘ก and ๐œ(๐‘ก)=๐‘ก, respectively. Examples are inserted to show how impulsive perturbations greatly affect the oscillation behavior of the solutions.