Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Research Article Existence and Lyapunov Stability of Periodic Solutions for Generalized Higher-Order Neutral Differential Equations | Hindawi Publishing Corporation Boundary Value Problems Volume 2011 Article ID 635767 21 pages doi 2011 635767 Research Article Existence and Lyapunov Stability of Periodic Solutions for Generalized Higher-Order Neutral Differential Equations Jingli Ren 1 Wing-Sum Cheung 2 and Zhibo Cheng1 1 Department of Mathematics Zhengzhou University Zhengzhou 450001 China 2 Department of Mathematics The University of Hong Kong Pokfulam Road Hong Kong Correspondence should be addressed to Wing-Sum Cheung wscheung@ Received 17 May 2010 Accepted 23 June 2010 Academic Editor Feliz Manuel Minhós Copyright 2011 Jingli Ren 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. Existence and Lyapunov stability of periodic solutions for a generalized higher-order neutral differential equation are established. 1. Introduction In recent years there is a good amount of work on periodic solutions for neutral differential equations see 1-11 and the references cited therein . For example the following neutral differential equations d u f - ku t - t g1 u f g2 u f - T1 p t ou x f cx f - r f x f g x f - t f p f x t - cx t - ơyA1 f x f x f gi f x t s da s j p f -r have been studied in 1 3 8 respectively and existence criteria of periodic solutions were established for these equations. Afterwards along with intensive research on the p-Laplacian 2 Boundary Value Problems some authors 4 11 start to consider the following p-Laplacian neutral functional differential equations ệp x t - cx t - Ơ g t x t - T t p t ệp xạ - cx f - Ơ f x ạ g xụ - T i e t and by using topological degree theory and some analysis skills existence results of periodic solutions for have been presented. In general most of the existing results are concentrated on lower-order neutral functional differential equations while studies on higher-order
