Electron. J. Diff. Equ., Vol. 2014 (2014), No. 186, pp. 1-12.

Asymptotic behavior of solutions to higher order nonlinear delay differential equations

Haihua Liang

In this article, we study the oscillation and asymptotic behavior of solutions to the nonlinear delay differential equation
By using a generalized Riccati transformation and an integral averaging technique, we establish sufficient conditions for all solutions to oscillate, or to converge to zero. Especially when the delay has the form $g(t)=at-\tau$, we provide two convenient oscillatory criteria. Some examples are given to illustrate our results.

Submitted June 27, 2014. Published September 3, 2014.
Math Subject Classifications: 34K11, 34K25.
Key Words: Higher order differential equation; delay differential equation, asymptotic behavior; oscillation.

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Haihua Liang
Department of Computer Science
Guangdong Polytechnic Normal University
Guangzhou, Guangdong 510665, China
email: haiihuaa@tom.com

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