Positive solutions of three-point nonlinear second order boundary value problem

Y. Raffoul, University of Dayton, Dayton, U.S.A.

E. J. Qualitative Theory of Diff. Equ., No. 15. (2002), pp. 1-11.

Abstract: In this paper we apply a cone theoretic fixed point theorem and obtain conditions for the existence of positive solutions to the three-point nonlinear second order boundary value problem
$$ u''(t)+\lambda a(t)f(u(t)) = 0, \;\;\;t\in(0,1)$$
$$u(0)=0,\;\;\;\; \alpha u(\eta)=u(1),$$
where $0<\eta<1$ and $0<\alpha <\frac{1}{\eta}.$

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