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 Exponential Stability of Difference Equations with Several Delays: Recursive Approach | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 104310 13 pages doi 2009 104310 Research Article Exponential Stability of Difference Equations with Several Delays Recursive Approach Leonid Berezansky1 and Elena Braverman2 1 Department of Mathematics Ben-Gurion University of the Negev Beer-Sheva 84105 Israel 2 Department of Mathematics and Statistics University of Calgary 2500 University Drive . Calgary AB Canada T2N1N4 Correspondence should be addressed to Elena Braverman maelena@ Received 8 January 2009 Revised 16 April 2009 Accepted 23 April 2009 Recommended by Istvan Gyori We obtain new explicit exponential stability results for difference equations with several variable delays and variable coefficients. Several known results such as Clark s asymptotic stability criterion are generalized and extended to a new class of equations. Copyright 2009 L. Berezansky and E. Braverman. 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. 1. Introduction and Preliminaries In this paper we study stability of a scalar linear difference equation with several delays m xfn 1 - x n al n x hi nf hl n n n n0 i 1 where hl n is an integer for any l 1 . m n is an integer n0 0. Stability of and relevant nonlinear equations has been an intensively developed area during the last two decades. Let us compare stability methods for delay differential equations and delay difference equations. Many of the methods previously used for differential equations have also been applied to difference equations. However there are at least two methods which are specific for difference equations. The first approach is reducing a solution of a delay difference equation to the values of a solution of a delay differential equation with piecewise constant arguments at integer .
