Oscillation of Fourth-Order Delay Dynamic Equations


This paper is concerned with oscillatory behavior of a class of fourth-order delay dynamic equations on a time scale. In the general time scales case, four oscillation theorems are presented that can be used in cases where known results fail to apply. The results obtained can be applied to an equation which is referred to as Swift-Hohenberg delay equation on a time scale. These criteria improve a number of related contributions to the subject. Some illustrative examples are provided.


Mathematics and Statistics


This work was supported by National Key Basic Research Program of China (Grant No. 2013CB035604) and National Natural Science Foundation of China (Grant Nos. 61034007, 51277116 and 51107069). The authors express their sincere gratitude to the anonymous referees for the careful reading of the original manuscript and useful comments that helped to improve the presentation of the results and accentuate important details.

Keywords and Phrases

Delay dynamic equation; Fourth-order; Oscillation; Swift-Hohenberg equation; Time scale

International Standard Serial Number (ISSN)

1674-7283; 1869-1862

Document Type

Article - Journal

Document Version


File Type





© 2014 Science China Press and Springer-Verlag Berlin Heidelberg, All rights reserved.

Publication Date

01 Jan 2015