Electron. J. Diff. Equ., Vol. 2011 (2011), No. 14, pp. 1-14.

Positive solutions to generalized second-order three-point integral boundary-value problems

Saowaluk Chasreechai, Jessada Tariboon

Abstract:
In this article, by using Krasnoselskii's fixed point theorem, we obtain single and multiple positive solutions to the nonlinear second-order three-point integral boundary value problem
$$\displaylines{ u''(t)+a(t)f(u(t))=0,\quad 0<t<T, \cr u(0)=\beta\int_0^{\eta}u(s)ds,\quad \alpha\int_0^{\eta}u(s)ds=u(T), }$$
where $0<\eta<T$, $0<\alpha<\frac{2T}{\eta^2}$, $0<\beta<\frac{2T-\alpha\eta^2}{\eta(2T-\eta)}$ are given constants. As an application, we give some examples that illustrate our results.

Submitted October 22, 2010. Published January 26, 2011.
Math Subject Classifications: 34B15, 34K10.
Key Words: Positive solution; three-point boundary value problem; fixed point theorem; cone.

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Saowaluk Chasreechai
Department of Mathematics, Faculty of Applied Science
King Mongkut's University of Technology North Bangkok
Bangkok 10800, Thailand
email: slc@kmutnb.ac.th
Jessada Tariboon
Department of Mathematics, Faculty of Applied Science
King Mongkut's University of Technology North Bangkok
Bangkok 10800, Thailand.
Centre of Excellence in Mathematics, CHE,
Sri Ayutthaya Road, Bangkok 10400, Thailand
email: jessadat@kmutnb.ac.th

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