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Báo cáo hóa học: "Research Article Existence of Positive Solutions for Multipoint Boundary Value Problem on the Half-Line with Impulses"

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 Existence of Positive Solutions for Multipoint Boundary Value Problem on the Half-Line with Impulses | Hindawi Publishing Corporation Boundary Value Problems Volume 2009 Article ID 834158 12 pages doi 10.1155 2009 834158 Research Article Existence of Positive Solutions for Multipoint Boundary Value Problem on the Half-Line with Impulses Jianli Li1 and Juan J. Nieto2 1 Department of Mathematics Hunan Normal University Changsha Hunan 410081 China 2 Departamento de Analisis Matemứtico Facultad de Matemứticas Universidad de Santiago de Compostela 15782 Santiago de Compostela Spain Correspondence should be addressed to Jianli Li ljianli@sina.com Received 7 March 2009 Revised 18 April 2009 Accepted 25 April 2009 Recommended by Donal O Regan We consider a multi-point boundary value problem on the half-line with impulses. By using a fixed-point theorem due to Avery and Peterson the existence of at least three positive solutions is obtained. Copyright 2009 J. Li and J. J. Nieto. 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 differential equations are a basic tool to study evolution processes that are subjected to abrupt changes in their state. For instance many biological physical and engineering applications exhibit impulsive effects see 1-3 . It should be noted that recent progress in the development of the qualitative theory of impulsive differential equations has been stimulated primarily by a number of interesting applied problems 4-24 . In this paper we consider the existence of multiple positive solutions of the following impulsive boundary value problem for short BVP on a half-line u 1 q t f t u 0 0 t t ftk àu tk Ik u tk k 1 . p m-2 u 0 y aiu fi u x 0 i 1 1.1 2 Boundary Value Problems where u to limt TOu f 0 Ỉ1 Ỉ2 ịm-2 TO 0 fl t2 tp TO Auựk u fi - u f- and ữị f q and Ik satisfy H1 0 Em-2 ai 1 H2 f t ù e C 0 to x 0 to 0 to Ik u e C 0 to 0 to and whenu 1 f is bounded f t ù and Ik u