tailieunhanh - Báo cáo hóa học: " Research Article Multiple Positive Solutions for a Class of m-Point Boundary Value Problems 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 Multiple Positive Solutions for a Class of m-Point Boundary Value Problems on Time Scales | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 219251 14 pages doi 2009 219251 Research Article Multiple Positive Solutions for a Class of m-Point Boundary Value Problems on Time Scales Meiqiang Feng 1 Xuemei Zhang 2 3 and Weigao Ge3 1 School of Science Beijing Information Science Technology University Beijing 100192 China 2 Department of Mathematics and Physics North China Electric Power University Beijing 102206 China 3 Department of Applied Mathematics Beijing Institute of Technology Beijing 100081 China Correspondence should be addressed to Xuemei Zhang zxm74@ Received 1 December 2008 Revised 15 April 2009 Accepted 10 June 2009 Recommended by Victoria Otero-Espinar By constructing an available integral operator and combining Krasnosel skii-Zabreiko fixed point theorem with properties of Green s function this paper shows the existence of multiple positive solutions for a class of m-point second-order Sturm-Liouville-like boundary value problems on time scales with polynomial nonlinearity. The results significantly extend and improve many known results for both the continuous case and more general time scales. We illustrate our results by one example which cannot be handled using the existing results. Copyright 2009 Meiqiang Feng 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. 1. Introduction Recently there have been many papers working on the existence of positive solutions to boundary value problems for differential equations on time scales see for example fl-20 . This has been mainly due to its unification of the theory of differential and difference equations. An introduction to this unification is given in 11 12 18 19 . Now this study is still a new area of fairly theoretical exploration in mathematics. However it has led to several .