Báo cáo hóa học: " Research Article On the Spectrum of Almost Periodic Solution of Second-Order Neutral Delay Differential Equations with Piecewise Constant of Argument"

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 On the Spectrum of Almost Periodic Solution of Second-Order Neutral Delay Differential Equations with Piecewise Constant of Argument | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 143175 14 pages doi 2009 143175 Research Article On the Spectrum of Almost Periodic Solution of Second-Order Neutral Delay Differential Equations with Piecewise Constant of Argument Li Wang and Chuanyi Zhang Department of Mathematics Harbin Institute of Technology Harbin 150001 China Correspondence should be addressed to Li Wang wanglimath@ Received 16 December 2008 Accepted 10 April 2009 Recommended by Ondrej Dosly The spectrum containment of almost periodic solution of second-order neutral delay differential equations with piecewise constant of argument EPCA for short of the form x t px t - 1 qx 2 t 1 2 f t is considered. The main result obtained in this paper is different from that given by some authors for ordinary differential equations ODE for short and clearly shows the differences between ODE and EPCA. Moreover it is also different from that given for equation x t px t - 1 qx t f t because of the difference between t and 2 t 1 2 . Copyright 2009 L. Wang and C. Zhang. 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 Some Preliminaries Differential equations with piecewise constant argument which were firstly considered by Cooke and Wiener 1 and Shah and Wiener 2 combine properties of both differential and difference equations and usually describe hybrid dynamical systems and have applications in certain biomedical models in the work of Busenberg and Cooke 3 . Over the years more attention has been paid to the existence uniqueness and spectrum containment of almost periodic solutions of this type of equations see . 4-12 and reference there in . If gi t and g2 t are almost periodic then the module containment property mod gi c mod g2 can be characterized in several ways see

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