Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Positive periodic solution of higher-order functional difference equation | Tang and Liu Advances in Difference Equations 2011 2011 56 http content 2011 1 56 o Advances in Difference Equations a SpringerOpen Journal RESEARCH Open Access Positive periodic solution of higher-order functional difference equation Mei-Lan Tang and Xin-Ge Liu Correspondence liuxgliuhua@ School of Mathematical Science and Computing Technology Central South University Changsha Hunan 410083 China Springer Abstract Based on a fixed point theorem in a cone a new sufficient condition for the existence of a positive periodic solution to a class of higher-order functional difference equations is established in this article. The result obtained in this article is different from the existing results in previous literature. Mathematic Subject Classification 2000 34k13 MSC 39A70. Keywords positive periodic solution fixed point theorem cone existence 1 Introduction The existence of positive periodic solutions of discrete mathematical models such as the discrete model of blood cell production and the single-species discrete periodic population model has been studied extensively in recent years see 1-8 for example . Most of these discrete mathematical models are first-order functional difference equations. Relatively few articles focused on the existence of positive periodic solutions of higher-order functional difference equations. In 2010 Wang and Chen 9 have studied the existence of positive periodic solutions for the following general higher-order functional difference equation x n m k ax n m bx n k abx n f n x n T n 1 where a 1 b 1 are positive constants t Z Z and ĩ n m r n f n m u f n u for any u e R m m k e N where N denotes the set of positive integers. Based on fixed point theorem in a cone 10 11 some new sufficient conditions on the existence of positive periodic solutions to the higher-order functional difference equation 1 are obtained. However the main results in 9 require that a should be positive constant l should .
