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Báo cáo hoa học: " Research Article Existence of Nonoscillatory Solutions to Second-Order Neutral Delay Dynamic Equations on Time Scales"

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 Existence of Nonoscillatory Solutions to Second-Order Neutral Delay Dynamic Equations on Time Scales | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 562329 10 pages doi 10.1155 2009 562329 Research Article Existence of Nonoscillatory Solutions to Second-Order Neutral Delay Dynamic Equations on Time Scales Tongxing Li 1 Zhenlai Han 1 2 Shurong Sun 1 3 and Dianwu Yang1 1 School of Science University of Jinan Jinan Shandong 250022 China 2 School of Control Science and Engineering Shandong University Jinan Shandong 250061 China 3 Department of Mathematics and Statistics Missouri University of Science and Technology Rolla mO 65409-0020 USA Correspondence should be addressed to Zhenlai Han hanzhenlai@163.com Received 5 March 2009 Revised 24 June 2009 Accepted 24 August 2009 Recommended by Alberto Cabada We employ Kranoselskii s fixed point theorem to establish the existence of nonoscillatory solutions to the second-order neutral delay dynamic equation x t p t x Tg t AA qi t x ri t -q2 t x T2 t e t on a time scale T. To dwell upon the importance of our results one interesting example is also included. Copyright 2009 Tongxing Li 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. 1. Introduction The theory of time scales which has recently received a lot of attention was introduced by Hilger in his Ph.D. Thesis in 1988 in order to unify continuous and discrete analysis see Hilger 1 . Several authors have expounded on various aspects of this new theory see the survey paper by Agarwal et al. 2 and references cited therein. A book on the subject of time scales by Bohner and Peterson 3 summarizes and organizes much of the time scale calculus we refer also to the last book by Bohner and Peterson 4 for advances in dynamic equations on time scales. For the notation used below we refer to the next section that provides some basic facts on time scales extracted from Bohner and .