Electron. J. Diff. Eqns., Vol. 2008(2008), No. 41, pp. 1-7.

Existence of positive solution for semipositone second-order three-point boundary-value problem

Jian-Ping Sun, Jia Wei

Abstract:
In this paper, we establish the existence of positive solution for the semipositone second-order three-point boundary value problem $u''(t)+\lambda f(t,u(t))=0$, $0<t<1$, $u(0)=\alpha u(\eta)$, $ u(1)=\beta u(\eta)$. Our arguments are based on the well-known Guo-Krasnosel'skii fixed-point theorem in cones.

Submitted August 28, 2007. Published March 20, 2008.
Math Subject Classifications: 34B15.
Key Words: Semipositone; boundary value problem; positive solution; existence; fixed-point.

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Jian-Ping Sun
Department of Applied Mathematics
Lanzhou University of Technology
Lanzhou, Gansu, 730050, China
email: jpsun@lut.cn
Jia Wei
Department of Applied Mathematics
Lanzhou University of Technology
Lanzhou, Gansu, 730050, China
email: weijia_vick@163.com

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