Abstract and Applied Analysis

Oscillation for Third-Order Nonlinear Differential Equations with Deviating Argument

Miroslav Bartušek, Mariella Cecchi, Zuzana Došlá, and Mauro Marini

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Abstract

We study necessary and sufficient conditions for the oscillation of the third-order nonlinear ordinary differential equation with damping term and deviating argument ${x}^{{'''}}(t)+q(t){x}^{\prime }(t)+r(t)f(x(\varphi (t)))=0$. Motivated by the work of Kiguradze (1992), the existence and asymptotic properties of nonoscillatory solutions are investigated in case when the differential operator $\mathcal{L}x={x}^{{'''}}+q(t){x}^{\prime }$ is oscillatory.

Article information

Source
Abstr. Appl. Anal. Volume 2010 (2010), Article ID 278962, 19 pages.

Dates
First available in Project Euclid: 2 March 2010

Permanent link to this document
http://projecteuclid.org/euclid.aaa/1267538586

Digital Object Identifier
doi:10.1155/2010/278962

Mathematical Reviews number (MathSciNet)
MR2587610

Zentralblatt MATH identifier
1192.34073

Citation

Bartušek, Miroslav; Cecchi, Mariella; Došlá, Zuzana; Marini, Mauro. Oscillation for Third-Order Nonlinear Differential Equations with Deviating Argument. Abstr. Appl. Anal. 2010 (2010), Article ID 278962, 19 pages. doi:10.1155/2010/278962. http://projecteuclid.org/euclid.aaa/1267538586.


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