Electron. J. Diff. Eqns., Vol. 2000(2000), No. 65, pp. 1-8.

Positive solutions to a second order multi-point boundary-value problem

Daomin Cao & Ruyun Ma

We prove the existence of positive solutions to the boundary-value problem
$ u''+\lambda a(t)f(u,u')=0 $
$ u(0)=0,\quad u(1)=\sum^{m-2}_{i=1} a_i u(\xi_i) $ ,
where $a$ is a continuous function that may change sign on [0,1], $f$ is a continuous function with $f(0,0)>0$, and $\lambda$ is a samll positive constant. For finding solutions we use the Leray-Schauder fixed point theorem.

Submitted September 18, 2000. Published October 30, 2000.
Math Subject Classifications: 34B10.
Key Words: Multi-point boundary value problem, positive solution, fixed point theorem.

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Daomin Cao
Institute of Applied Mathematics
Academy of Mathematics and System Sciences
Beijing 100080, People's Republic of China
email: cao@amath6.amt.ac.cn
Ruyun Ma
Department of Mathematics
Northwest Normal University
Lanzhou 730070, Gansu, P. R. China
email: mary@nwnu.edu.cn

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