Abstract and Applied Analysis

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

Yuzhen Bai and Lihua Liu

Full-text: Open access

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).

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 564068, 11 pages.

Dates
First available in Project Euclid: 1 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1288620736

Digital Object Identifier
doi:10.1155/2010/564068

Mathematical Reviews number (MathSciNet)
MR2660395

Zentralblatt MATH identifier
1205.34078

Citation

Bai, Yuzhen; Liu, Lihua. New Oscillation Criteria for Second-Order Neutral Delay Differential Equations with Positive and Negative Coefficients. Abstr. Appl. Anal. 2010 (2010), Article ID 564068, 11 pages. doi:10.1155/2010/564068. https://projecteuclid.org/euclid.aaa/1288620736


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