Journal of Inequalities and Applications
Volume 2011 (2011), Article ID 979705, 27 pages
doi:10.1155/2011/979705
Research Article

Lyapunov Stability of Quasilinear Implicit Dynamic Equations on Time Scales

N. H. Du,1 N. C. Liem,1 C. J. Chyan,2 and S. W. Lin2

1Department of Mathematics, Mechanics and Informatics, Vietnam National University, 334 Nguyen Trai, Hanoi, Vietnam
2Department of Mathematics, Tamkang University, 151 Ying Chuang Road, Tamsui, Taipei County 25317, Taiwan

Received 29 September 2010; Accepted 4 February 2011

Academic Editor: Stevo Stevic

Copyright © 2011 N. H. Du et al. 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

This paper studies the stability of the solution 𝑥 ≡ 0 for a class of quasilinear implicit dynamic equations on time scales of the form 𝐴 𝑡 𝑥 Δ = 𝑓 ( 𝑡 , 𝑥 ) . We deal with an index concept to study the solvability and use Lyapunov functions as a tool to approach the stability problem.