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Báo cáo hóa học: " Research Article Lyapunov Stability of Quasilinear Implicit Dynamic Equations on Time Scales"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Lyapunov Stability of Quasilinear Implicit Dynamic Equations on Time Scales | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 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 1 Department of Mathematics Mechanics and Informatics Vietnam National University 334 Nguyen Trai Hanoi Vietnam 2 Department of Mathematics Tamkang University 151 Ying Chuang Road Tamsui Taipei County 25317 Taiwan Correspondence should be addressed to N. H. Du dunh@vnu.edu.vn 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. This paper studies the stability of the solution x 0 for a class of quasilinear implicit dynamic equations on time scales of the form AtxÁ 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. 1. Introduction The stability theory of quasilinear differential-algebraic equations DAEs for short Atx t f t x t x t f t 0 0 0 vt eR 1.1 with A. being a given m X m-matrix function has been an intensively discussed field in both theory and practice. This problem can be seen in many real problems such as in electric circuits chemical reactions and vehicle systems. Marz in 1 has dealt with the question whether the zero-solution of 1.1 is asymptotically stable in the Lyapunov sense with f t x t x t Bx f g t x f x ff with A being constant and small perturbation g. Together with the theory of DAEs there has been a great interest in singular difference equation SDE also referred to as descriptor systems implicit difference equations Anx n 1 f n x n 1 x n n Si. 1.2 2 Journal of Inequalities and Applications This model appears in many .