Journal of Applied Mathematics
Volume 2011 (2011), Article ID 418136, 10 pages
http://dx.doi.org/10.1155/2011/418136
Research Article

Lyapunov-Type Inequalities for Some Quasilinear Dynamic System Involving the ( 𝑝 1 , 𝑝 2 , … , 𝑝 𝑚 ) -Laplacian on Time Scales

Xiaofei He1 and Qi-Ming Zhang2

1College of Mathematics and Computer Science, Jishou University, Jishou 416000, Hunan, China
2College of Science, Hunan University of Technology, Zhuzhou 412007, Hunan, China

Received 30 June 2011; Accepted 25 August 2011

Academic Editor: Yansheng Liu

Copyright © 2011 Xiaofei He and Qi-Ming Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We establish several new Lyapunov-type inequalities for some quasilinear dynamic system involving the ( 𝑝 1 , 𝑝 2 , … , 𝑝 𝑚 ) -Laplacian on an arbitrary time scale 𝕋 , which generalize and improve some related existing results including the continuous and discrete cases.