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 Oscillation of Solutions of a Linear Second-Order Discrete-Delayed Equation | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 693867 12 pages doi 2010 693867 Research Article Oscillation of Solutions of a Linear Second-Order Discrete-Delayed Equation J. Bastinec 1 J. Diblik 1 2 and Z. Smarda1 1 Department of Mathematics Faculty of Electrical Engineering and Communication Brno University of Technology 61600 Brno Czech Republic 2 Brno University of Technology Brno Czech Republic Correspondence should be addressed to J. Diblik Received 5 January 2010 Accepted 31 March 2010 Academic Editor Leonid Berezansky Copyright 2010 J. Bastinec 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. A linear second-order discrete-delayed equation Ax n -p n x n - 1 with a positive coefficient p is considered for n OT. This equation is known to have a positive solution if p fulfils an inequality. The goal of the paper is to show that in the case of the opposite inequality for p all solutions of the equation considered are oscillating for n OT. 1. Introduction The existence of a positive solution of difference equations is often encountered when analysing mathematical models describing various processes. This is a motivation for an intensive study of the conditions for the existence of positive solutions of discrete or continuous equations. Such analysis is related to an investigation of the case of all solutions being oscillating for relevant investigation in both directions we refer . to 1-15 and to the references therein . In this paper sharp conditions are derived for all the solutions being oscillating for a class of linear second-order delayed-discrete equations. We consider the delayed second-order linear discrete equation Ax n -p n x n - 1 where n e Zf a a 1 . a e N is fixed Ax n x n 1 - x n and p Zf R 0 x . A .
