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Abstract and Applied Analysis
Volume 2011 (2011), Article ID 367541, 17 pages
http://dx.doi.org/10.1155/2011/367541
Research Article

Oscillation Criteria for Second-Order Superlinear Neutral Differential Equations

1School of Science, University of Jinan, Jinan, Shandong 250022, China
2School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, China

Received 5 September 2010; Accepted 20 January 2011

Academic Editor: Josef Diblรญk

Copyright ยฉ 2011 Tongxing Li 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

Some oscillation criteria are established for the second-order superlinear neutral differential equations ( ๐‘Ÿ ( ๐‘ก ) | ๐‘ง โ€ฒ ( ๐‘ก ) | ๐›ผ โˆ’ 1 ๐‘ง โ€ฒ ( ๐‘ก ) ) โ€ฒ + ๐‘“ ( ๐‘ก , ๐‘ฅ ( ๐œŽ ( ๐‘ก ) ) ) = 0 , ๐‘ก โ‰ฅ ๐‘ก 0 , where ๐‘ง ( ๐‘ก ) = ๐‘ฅ ( ๐‘ก ) + ๐‘ ( ๐‘ก ) ๐‘ฅ ( ๐œ ( ๐‘ก ) ) , ๐œ ( ๐‘ก ) โ‰ฅ ๐‘ก , ๐œŽ ( ๐‘ก ) โ‰ฅ ๐‘ก , ๐‘ โˆˆ ๐ถ ( [ ๐‘ก 0 , โˆž ) , [ 0 , ๐‘ 0 ] ) , and ๐›ผ โ‰ฅ 1 . Our results are based on the cases โˆซ โˆž ๐‘ก 0 1 / ๐‘Ÿ 1 / ๐›ผ ( ๐‘ก ) d ๐‘ก = โˆž or โˆซ โˆž ๐‘ก 0 1 / ๐‘Ÿ 1 / ๐›ผ ( ๐‘ก ) d ๐‘ก < โˆž . Two examples are also provided to illustrate these results.