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Báo cáo hóa học: "EXISTENCE OF POSITIVE SOLUTION FOR SECOND-ORDER IMPULSIVE BOUNDARY VALUE PROBLEMS ON INFINITY INTERVALS"

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: EXISTENCE OF POSITIVE SOLUTION FOR SECOND-ORDER IMPULSIVE BOUNDARY VALUE PROBLEMS ON INFINITY INTERVALS | EXISTENCE OF POSITIVE SOLUTION FOR SECOND-ORDER IMPULSIVE BOUNDARY VALUE PROBLEMS ON INFINITY INTERVALS JIANLI LI AND JIANHUA SHEN Received 8 January 2006 Revised 2 September 2006 Accepted 4 September 2006 We deal with the existence of positive solutions to impulsive second-order differential equations subject to some boundary conditions on the semi-infinity interval. Copyright 2006 J. Li and J. Shen. 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 In recent years impulsive differential equations have become a very active area of research and we refer the reader to the monographs 8 and the articles 6 9 10 14 15 where properties of their solutions are studied and extensive bibliographies are given. In consequence it is very important to develop a complete basic theory of impulsive differential equations. Also infinite interval problems have been extensive studied see 1-5 11 12 . In this paper we study the existence of positive solutions for the following boundary value problem BVP with impulses y g t y y 0 0 t to t tk A y tk bky ltk A y tk aky tk k 1 2 . 1.1 y 0 0 y bounded on 0 to where tk tk 1 limk TO tk to ay tk y t - y tk Ay tk y t - y t- andg is continuous except tk X R X R we assume that for k e N 1 2 . andx y e R there exist the limits lint- g t x y g tk x y lint g t x y . 1.2 - 1 - i The problems of the above type without impulses have been discussed by several authors in the literature we refer the reader to the pioneer works of Agarwal and O Regan 1 2 4 and Ma 12 and Constantin 11 . But as far as we know the publication on solvability of infinity interval problems with impulses is fewer 15 . In this paper we want to Hindawi Publishing Corporation Boundary Value Problems Volume 2006 Article ID 14594 Pages 1-11 DOI 10.1155 BVP 2006 14594 2 Existence of positive solution for IBVP on