Positive solutions for second-order m-point boundary value problems

Authors:
Yanping Guo;Wenrui Shan;Weigao Ge
Affiliations:
Department of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, People's Republic of China and College of Sciences, Hebei University of Science and Technology, Shijiazhuang, He ...;Department of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, People's Republic of China;Department of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, People's Republic of China
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

Citing 2
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Symmetric positive solutions for p-Laplacian fourth-order differential equations with integral boundary conditions

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Existence of solutions of boundary value problems with integral boundary conditions for second-order impulsive integro-differential equations in Banach spaces

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Existence results for n-point boundary value problem of second order ordinary differential equations

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A fourth-order compact finite difference method for nonlinear higher-order multi-point boundary value problems

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Positive solutions for a system of higher-order multi-point boundary value problems

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Positive solutions for an n-point nonhomogeneous boundary value problem

Mathematical and Computer Modelling: An International Journal

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Abstract

By using the Schauder fixed point theorem and analysis method, we establish the existence of solutions for the m-point boundary value problem u"(t) + a(t)f(u) = 0, u(0)= 0, u(1) - Σi=1m-2kiu(ξi) = b, where b, ki 0 (i = 1,2,...,m - 2),0 1 2 m-2 a(t) is allowed to be singular at t = 0,1. Under some conditions, we show that there exists a positive number b* such that the problem has at least one positive solution for 0 b b* and no solution for b b*.