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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 Solvability of a Higher-Order Nonlinear Neutral Delay Difference Equation | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 767620 14 pages doi 10.1155 2010 767620 Research Article Solvability of a Higher-Order Nonlinear Neutral Delay Difference Equation Min Liu and Zhenyu Guo School of Sciences Liaoning Shihua University Fushun Liaoning 113001 China Correspondence should be addressed to Zhenyu Guo guozy@163.com Received 19 March 2010 Revised 10 July 2010 Accepted 5 September 2010 Academic Editor S. Grace Copyright 2010 M. Liu and Z. Guo. 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. The existence of bounded nonoscillatory solutions of a higher-order nonlinear neutral delay difference equationA akn A a2 A a1 A x bnxn-d f n x -r1n x -r2n . . x -rsn 0 n n0 where n0 0 d 0 k 0 and s 0 are integers ain n i 1 2 . k and bn n n are real sequences U. I rn . . c Z and f n n n0 x Rs R is a mapping is studied. Some sufficient conditions for the existence of bounded nonoscillatory solutions of this equation are established by using Schauder fixed point theorem and Krasnoselskii fixed point theorem and expatiated through seven theorems according to the range of value of the sequence bn n n . Moreover these sufficient conditions guarantee that this equation has not only one bounded nonoscillatory solution but also uncountably many bounded nonoscillatory solutions. 1. Introduction and Preliminaries Recently the interest in the study of the solvability of difference equations has been increasing see 1-17 and references cited therein . Some authors have paied their attention to various difference equations. For example A an Axn pnxgn 0 n 0 see 14 A anAxn qnxn 1 A anAxn qnf xn 1 n 0 1.1 1.2 2 Advances in Difference Equations see 11 A2 xn pxn-m PnXn-k - qnXn-l 0 n no 1.3 see 6 A2 xn pxn-k f n Xn 0 n 1 1.4 see 10 A2 Xn - pXn-T f n n0 1.5 i 1 see 9 A anA xn .
