Electron. J. Diff. Eqns., Vol. 1999(1999), No. 34, pp. 1-8.

Positive solutions for a nonlinear three-point boundary-value problem

Ruyun Ma

We study the existence of positive solutions to the boundary-value problem
 $ u''+a(t)f(u)=0,\quad t\in (0,1)$
 $u(0)=0,\quad\alpha u(\eta)=u(1)\,, $
where 0 less than \eta less than 1 and 0 less than \alpha less than 1/\eta. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem in cones.

Submitted June 9, 1999. Published September 15, 1999.
Math Subject Classifications: 34B15
Key Words: Second-order multi-point BVP, positive solution, cone, fixed point.

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Ruyun Ma
Department of Mathematics
Northwest Normal University
Lanzhou 730070, Gansu, P. R. China
e-mail address: mary@nwnu.edu.cn

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