tailieunhanh - báo cáo hóa học:" Research Article Multiple Positive Solutions for m-Point Boundary Value Problem 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 m-Point Boundary Value Problem on Time Scales | Hindawi Publishing Corporation Boundary Value Problems Volume 2011 Article ID 591219 11 pages doi 2011 591219 Research Article Multiple Positive Solutions for m-Point Boundary Value Problem on Time Scales Jie Liu1 2 and Hong-Rui Sun2 1 Department of Applied Mathematics Lanzhou University of Technology Lanzhou Gansu 730050 China 2 School of Mathematics and Statistics Lanzhou University Lanzhou Gansu 730000 China Correspondence should be addressed to Hong-Rui Sun hrsun@ Received 29 May 2010 Accepted 6 August 2010 Academic Editor Feliz Manuel Minhos Copyright 2011 J. Liu 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. The purpose of this article is to establish the existence of multiple positive solutions of the dynamic equation on time scales f wA t V h f f t u t u tf 0 t e 0 T t subject to the multipoint boundary condition MA 0 0 u T 2mi2 aiu ỉi where f R R is an increasing homeomorphism and satisfies the relation f xy f x ffy for x y e R which generalizes the usually p-Laplacian operator. An example applying the result is also presented. The main tool of this paper is a generalization of Leggett-Williams fixed point theorem and the interesting points are that the nonlinearity f contains the first-order derivative explicitly and the operator f is not necessarily odd. 1. Introduction The study of dynamic equations on time scales goes back to its founder Hilger 1 and is a new area of still fairly theoretical exploration in mathematics. On one hand the time scales approach not only unifies calculus and difference equations but also solves other problems that have a mix of stop-start and continuous behavior. On the other hand the time scales calculus has tremendous potential for application in biological phytoremediation of metals wound healing stock market and epidemic models