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

Abstract:
In this article, we study the oscillation and asymptotic behavior of solutions to the nonlinear delay differential equation
$$ x^{(n+3)}(t)+p(t)x^{(n)}(t)+q(t)f(x(g(t)))=0. $$
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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