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 Almost-Periodic Weak Solutions of Second-Order Neutral Delay-Differential Equations with Piecewise Constant Argument | Hindawi Publishing Corporation Advances in Difference Equations Volume 2008 Article ID 816091 11 pages doi 2008 816091 Research Article Almost-Periodic Weak Solutions of Second-Order Neutral Delay-Differential Equations with Piecewise Constant 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 10 December 2007 Accepted 4 June 2008 Recommended by Ondrej Dosly We investigate the existence of almost-periodic weak solutions of second-order neutral delaydifferential equations with piecewise constant argument of the form x t x t - 1 qx 2 t 1 2 f f where denotes the greatest integer function q is a real nonzero constant and f t is almost periodic. Copyright 2008 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 preliminaries Differential equations with piecewise constant argument which were firstly considered by Cooke and Wiener 1 and Shah and Wiener 2 usually describe hybrid dynamical systems a combination of continuous and discrete and so combine properties of both differential and difference equations. Over the years great attention has been paid to the study of the existence of almost-periodic-type solutions of this type of equations. There are many remarkable works on this field see 3-10 and references therein . Particularly the second-order neutral delaydifferential equations with piecewise constant argument of the form x J px j - 1 qx 2 t 1 2 f t have been intensively studied for p f 1 by different methods where denotes the greatest integer function p q are real nonzero constants and f t is almost periodic. In 6 Li introduced the concepts of odd-weak solution even-weak solution and weak solution of . Some .
