Oscillation Criteria for Second-Order Superlinear Neutral Differential Equations

Tongxing Li, Zhenlai Han, Chenghui Zhang and Hua Li

Abstract and Applied Analysis, 2011, vol. 2011, 1-17

Abstract:

Some oscillation criteria are established for the second-order superlinear neutral differential equations ( ð ‘Ÿ ( ð ‘¡ ) | 𠑧 ′ ( ð ‘¡ ) | ð ›¼ − 1 𠑧 ′ ( ð ‘¡ ) ) ′ + ð ‘“ ( ð ‘¡ , ð ‘¥ ( 𠜎 ( ð ‘¡ ) ) ) = 0 , ð ‘¡ ≥ ð ‘¡ 0 , where 𠑧 ( ð ‘¡ ) = ð ‘¥ ( ð ‘¡ ) + ð ‘ ( ð ‘¡ ) ð ‘¥ ( ð œ ( ð ‘¡ ) ) , ð œ ( ð ‘¡ ) ≥ ð ‘¡ , 𠜎 ( ð ‘¡ ) ≥ ð ‘¡ , ð ‘ âˆˆ ð ¶ ( [ ð ‘¡ 0 , ∞ ) , [ 0 , ð ‘ 0 ] ) , and ð ›¼ ≥ 1 . Our results are based on the cases ∫ ∞ ð ‘¡ 0 1 / ð ‘Ÿ 1 / ð ›¼ ( ð ‘¡ ) d ð ‘¡ = ∞ or ∫ ∞ ð ‘¡ 0 1 / ð ‘Ÿ 1 / ð ›¼ ( ð ‘¡ ) d ð ‘¡ < ∞ . Two examples are also provided to illustrate these results.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:367541

DOI: 10.1155/2011/367541

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