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New Oscillation Criteria for Second‐Order Neutral Delay Differential Equations with Positive and Negative Coefficients

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  • Yuzhen Bai
  • Lihua Liu

Abstract

We establish the oscillation and asymptotic criteria for the second‐order neutral delay differential equations with positive and negative coefficients having the forms [x(t) + ∑i∈Rci(t)x(αi(t))] ′′ + r(t)[x(t) + ∑i∈Rci(t)x(αi(t))] ′ + ∑i∈Ppi(t)x(βi(t)) − ∑i∈Qqi(t)x(γi(t)) = 0 and [x(t) + ∑i∈Rci(t)x(αi(t))] ′′ + r(t)[x(t) + ∑i∈Rci(t)x(αi(t))] ′ + ∑i∈Ppi(t)x(βi(t)) − ∑i∈Qqi(t)x(γi(t)) = f(t). The obtained new oscillation criteria extend and improve the recent results given in the paperof B. Karpuz et al. (2009).

Suggested Citation

  • Yuzhen Bai & Lihua Liu, 2010. "New Oscillation Criteria for Second‐Order Neutral Delay Differential Equations with Positive and Negative Coefficients," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    • Handle: RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:564068
    DOI: 10.1155/2010/564068
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    1. Jin-Zhu Zhang & Zhen Jin & Tie-Xiong Su & Jian-Jun Wang & Zhi-Yu Zhang & Ju-Rang Yan, 2008. "On the Nonoscillation of Second-Order Neutral Delay Differential Equation with Forcing Term," Discrete Dynamics in Nature and Society, Hindawi, vol. 2008, pages 1-9, March.
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