TAILIEUCHUNG - Báo cáo hóa học: " Multiple positive solutions for first-order impulsive integral 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: Multiple positive solutions for first-order impulsive integral boundary value problems on time scales | Li and Shu Boundary Value Problems 2011 2011 12 http content 2011 1 12 o Boundary Value Problems a SpringerOpen Journal RESEARCH Open Access Multiple positive solutions for first-order impulsive integral boundary value problems on time scales Yongkun Li and Jiangye Shu Correspondence yklie@. cn Department of Mathematics Yunnan University Kunming Yunnan 650091 People s Republic of China Springer Abstract In this paper we first present a class of first-order nonlinear impulsive integral boundary value problems on time scales. Then using the well-known Guo-Krasnoselskii fixed point theorem and Legget-Williams fixed point theorem some criteria for the existence of at least one two and three positive solutions are established for the problem under consideration respectively. Finally examples are presented to illustrate the main results. MSC 34B10 34B37 34N05. Keywords integral boundary value problem fixed point multiple solutions time scale 1 Introduction In fact continuous and discrete systems are very important in implementing and applications. It is well known that the theory of time scales has received a lot of attention which was introduced by Stefan Hilger in order to unify continuous and discrete analyses. Therefore it is meaningful to study dynamic systems on time scales which can unify differential and difference systems. In recent years a great deal of work has been done in the study of the existence of solutions for boundary value problems on time scales. For the background and results we refer the reader to some recent contributions 1-5 and references therein. At the same time boundary value problems for impulsive differential equations and impulsive difference equations have received much attention 6-12 since such equations may exhibit several real-world phenomena in physics biology engineering etc. see 13-15 and the references therein. In paper 16 Sun studied the first-order boundary value problem on time scales xA t f

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