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

Yuzhen Bai and Lihua Liu

Abstract and Applied Analysis, 2010, vol. 2010, 1-11

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 ∈ R c i ( t ) x ( α i ( t ) ) ] ′′ + r ( t ) [ x ( t ) + ∑ i ∈ R c i ( t ) x ( α i ( t ) ) ] ′ + ∑ i ∈ P p i ( t ) x ( β i ( t ) ) - ∑ i ∈ Q q i ( t ) x ( γ i ( t ) ) = 0 and [ x ( t ) + ∑ i ∈ R c i ( t ) x ( α i ( t ) ) ] ′′ + r ( t ) [ x ( t ) + ∑ i ∈ R c i ( t ) x ( α i ( t ) ) ] ′ + ∑ i ∈ P p i ( t ) x ( β i ( t ) ) - ∑ i ∈ Q q i ( t ) x ( γ i ( t ) ) = f ( t ) . The obtained new oscillation criteria extend and improve the recent results given in the paperof B. Karpuz et al. (2009).

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:564068

DOI: 10.1155/2010/564068

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