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Báo cáo hoa học: "Research Article Three Positive Periodic Solutions for a Class of Higher-Dimensional Functional Differential Equations with Impulses 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 Three Positive Periodic Solutions for a Class of Higher-Dimensional Functional Differential Equations with Impulses on Time Scales | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 698463 18 pages doi 10.1155 2009 698463 Research Article Three Positive Periodic Solutions for a Class of Higher-Dimensional Functional Differential Equations with Impulses on Time Scales Yongkun Li1 and Meng Hu1 2 1 Department of Mathematics Yunnan University Kunming Yunnan 650091 China 2 Department of Mathematics Anyang Normal University Anyang Henan 455000 China Correspondence should be addressed to Yongkun Li yklie@ynu.edu.cn Received 20 October 2009 Revised 29 November 2009 Accepted 1 December 2009 Recommended by Martin Bohner By using a multiple fixed point theorem Avery-Peterson fixed point theorem for cones some criteria are established for the existence of three positive periodic solutions for a class of higherdimensional functional differential equations with impulses on time scales of the following form xA t A t x t f t xt t tj t e T x tj x t- Ij x tj where A t aij tf nxn is a nonsingular matrix with continuous real-valued functions as its elements. Finally an example is presented to illustrate the feasibility and effectiveness of the results. Copyright 2009 Y. Li and M. Hu. 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 Impulsive delay differential equations may express several real-world simulation processes which depend on their prehistory and are subject to short-time disturbances. Such processes occur in the theory of optimal control population dynamics biotechnologies economics and so forth. Therefore the study of this class of dynamical systems has gained prominence and it is a rapidly growing field see for instance the monographs 1-4 and the references cited therein. Recently based on a fixed-point theorem in cones Li et al. 5 investigated the periodicity of the following scalar .