The existence of countably many positive solutions for some nonlinear nth order m-point boundary value problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:232

Article

Ji, Yude¹  Guo, Yanping¹ 

[1] Hebei Univ Sci & Technol, Coll Sci, Shijiazhuang 050018, Hebei, Peoples R China

关键词: Boundary value problem;    Green's function;    Krasnoselskii's fixed point theorem;    Holder's inequality;    Multiple positive solution;   

DOI  :  10.1016/j.cam.2009.05.023

来源: Elsevier

【 摘 要 】

In this paper, we consider the existence of countably many positive solutions for nth-order m-point boundary value problems consisting of the equation u(n)(t) + a(t)f(u(t)) = 0, t is an element of (0, 1), with one of the following boundary value conditions: u(0) = Sigma(m-2)(i=1) k(i)u(xi(i)), u'(0) = ... = u((n-2))(0) = 0, u(1) = 0, and u(0) = 0, u'(0) = ... = u((n-2))(0) = 0, u(1) = Sigma(m-2)(i=1) k(i)u(xi(i)), where n >= 2, k(i) > 0 (i = 1, 2,..., m - 2), 0 < xi(1) < xi(2) < ... < xi(m-2) < 1, a(t) is an element of L-p [0, 1] for some p >= 1 and has countably many singularities in [0, 1/2). The associated Green's function for the nth order m-point boundary value problem is first given, and we show that there exist countably many positive solutions using Holder's inequality and Krasnoselskii's fixed point theorem for operators on a cone. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.

【 授权许可】

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