Multiple Positive Solutions for Semi-positone m-point Boundary Value Problems

• Published in: Acta Mathematicae Applicatae Sinica Vol. 27; no. 3; pp. 419 - 426
• Main Authors: Zhai, Cheng-bo, Yang, Cheng
• Format: Journal Article
• Language: English
• Published: Heildeberg Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.07.2011
• Subjects: Applications of Mathematics; BIU; Math Applications in Computer Science; Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; m点边值问题; Theoretical; 不动点定理; 多重正解; 应用程序; 边界值问题; concave functional; Multiple positive solutions; parameter; 34B10; point boundary value problem; cone; semi-positone
• ISSN: 0168-9673; 1618-3932
• DOI: 10.1007/s10255-009-6180-3

In this article, we establish the existence of at least two positive solutions for the semi-positone m-point boundary value problem with a parameter u （t） ＋ λf （t, u） = 0, t ∈ （0, 1）, u （0） = sum （biu （ξ i ）） from i=1 to m-2, u（1）= sum （aiu（ξ i ）） from i=1 to m-2, where λ 〉 0 is a parameter, 0 〈 ξ 1 〈 ξ 2 〈 ··· 〈 ξ m 2 〈 1 with 0 〈sum ai from i=1 to m-2 〈 1, sum bi from i=1 to m-2 =1 b i 〈 1, a i , b i ∈ [0, ∞） and f （t, u） ≥ M with M is a positive constant. The method employed is the Leggett-Williams fixed-point theorem. As an application, an example is given to demonstrate the main result.