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 , 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
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