TAILIEUCHUNG - Báo cáo sinh học: "Research Article Monotone Iterative Technique for First-Order Nonlinear Periodic Boundary Value Problems on Time Scales"

Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Research Article Monotone Iterative Technique for First-Order Nonlinear Periodic Boundary Value Problems on Time Scales | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 620459 10 pages doi 2010 620459 Research Article Monotone Iterative Technique for First-Order Nonlinear Periodic Boundary Value Problems on Time Scales Ya-Hong Zhao and Jian-Ping Sun Department of Applied Mathematics Lanzhou University of Technology Lanzhou Gansu 730050 China Correspondence should be addressed to Jian-Ping Sun jpsun@ Received 12 February 2010 Revised 17 May 2010 Accepted 26 June 2010 Academic Editor Paul Eloe Copyright 2010 . Zhao and . Sun. 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. We investigate the following nonlinear first-order periodic boundary value problem on time scales xA t p t x ơ tỴ f t x t t e 0 T t x 0 x y T . Some new existence criteria of positive solutions are established by using the monotone iterative technique. 1. Introduction Recently periodic boundary value problems PBVPs for short for dynamic equations on time scales have been studied by several authors by using the method of lower and upper solutions fixed point theorems and the theory of fixed point index. We refer the reader to 1-10 for some recent results. In this paper we are interested in the existence of positive solutions for the following first-order PBVP on time scales xA t p t x ơ t f f x fỴ t e 0 T t 2. x 0 x ơ T where Ơ will be defined in Section 2 T is a time scale T 0 is fixed and 0 T e T. For each interval I of R we denote by IT I T. By applying the monotone iterative technique we obtain not only the existence of positive solution for the PBVP but also give an iterative scheme which approximates the solution. It is worth mentioning that the initial term of our iterative scheme is a constant function which implies that the iterative scheme is significant and feasible. For abstract

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