Positive solutions of singular three-point boundary value problems for second-order differential equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:230

Article

Sun, Yan¹  Liu, Lishan²  Zhang, Jizhou¹  Agarwal, R. P.³ 

[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[2] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China

[3] Florida Inst Technol, Dept Math Sci, Melbourne, FL USA

关键词: Positive solutions;    Three-point boundary value problem;    Singular-second-order differential equation;    Fixed point index;   

DOI  :  10.1016/j.cam.2009.01.003

来源: Elsevier

【 摘 要 】

In this paper, we study the existence of positive solutions of a singular three-point boundary value problem for the following second-order differential equation {y '' + mu a(t)f(t, y(t)) = 0, t is an element of (0, 1), y(0) - beta y'(0) = 0, y(1) = alpha y(eta), where mu > 0 is a parameter, beta > 0, 0 < eta < 1, 0 < alpha eta < 1, (1 - alpha eta) + beta(1 - alpha) > 0, By constructing an available integral operator and combining fixed point index theory with properties of Green's function under some conditions concerning the first eigenvalues corresponding to the relevant linear operator, the sufficient conditions of the existence of positive solutions for the boundary value problems are established. The interesting point of the results is that the term a(t) may be singular at t = 0 and/or t = 1, moreover the nonlinear f (t, x) is also allowed to have singularity at x = 0. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

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