tailieunhanh - Báo cáo hóa học: " Research Article Reducibility and Stability Results for Linear System of Difference Equations"

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 Reducibility and Stability Results for Linear System of Difference Equations | Hindawi Publishing Corporation Advances in Difference Equations Volume 2008 Article ID 867635 6 pages doi 2008 867635 Research Article Reducibility and Stability Results for Linear System of Difference Equations Aydin Tiryaki1 and Adil Misir2 1 Department of Mathematics and Computer Sciences Faculty of Arts and Science Izmir University 35340 Izmir Turkey 2 Department of Mathematics Faculty of Arts and Science Gazi University Teknikokullar 06500 Ankara Turkey Correspondence should be addressed to Adil Misir adilm@ Received 8 August 2008 Revised 22 October 2008 Accepted 29 October 2008 Recommended by Martin J. Bohner We first give a theorem on the reducibility of linear system of difference equations of the form x n 1 A n x n . Next by the means of Floquet theory we obtain some stability results. Moreover some examples are given to illustrate the importance of the results. Copyright 2008 A. Tiryaki and A. Misir. 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 Consider the homogeneous linear system of difference equations x n 1 Afn xfn n e N 0 1 2 . where A n aij n is a k X k nonsingular matrix with real entries and xfri x1 n x2 n . . xk n T e Rk. If for some n0 0 x no xo is specified then is called an initial value problem IVP . The solution of this IVP is given by n-1 x n no xo I J7IA i xo O n xo i no 2 Advances in Difference Equations where n is the fundamental matrix defined by n-1 i A n - 1 A n - 2 A n0 if n n0 H-i I no I if n n0. However is called reducible to equation y n 1 B n y n L5 if there is a nonsingular matrix H n with real entries such that x n H n y n . Let S n be a k X k matrix function whose entries are real-valued functions defined for n n0. Consider the system z n 1 S n z n n n0. Let H n be a fundamental matrix of .