Positive Solutions of a Weak Semipositone Third-Order Three-Point Boundary Value Problem  

作　　者：Qing Liu YAO 

机构地区：[1]Department of Applied Mathematics, Nanjing University of Finance and Economics, Jiangsu 210003, P. R. China

出　　处：《Journal of Mathematical Research and Exposition》2010年第1期173-180,共8页数学研究与评论（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No.10871059)

摘　　要：The positive solutions are studied for the nonlinear third-order three-point boundary value problem u′″（t）=f（t,u（t））,a.e,t∈[0,1],u（0）=u′（η）=u″（1）=0, where the nonlinear term f（t, u） is a Caratheodory function and there exists a nonnegative function h ∈ L^1[0, 1] such that f（t, u） 〉 ≥-h（t）. The existence of n positive solutions is proved by considering the integrations of ＂height functions＂ and applying the Krasnosel＇skii fixed point theorem on cone.The positive solutions are studied for the nonlinear third-order three-point boundary value problem u′″（t）=f（t,u（t））,a.e,t∈[0,1],u（0）=u′（η）=u″（1）=0, where the nonlinear term f（t, u） is a Caratheodory function and there exists a nonnegative function h ∈ L^1[0, 1] such that f（t, u） 〉 ≥-h（t）. The existence of n positive solutions is proved by considering the integrations of ＂height functions＂ and applying the Krasnosel＇skii fixed point theorem on cone.

关 键 词：singular ordinary differential equation multi-point boundary value problem posi-tive solution EXISTENCE multiplicity. 

分 类 号：O175.8[理学—数学] O175[理学—基础数学]