Geodesic
Positive solutions for systems of generalized three-point nonlinear boundary value problems
Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 1, pp. 79-91.

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Values of $\lambda$ are determined for which there exist positive solutions of the system of three-point boundary value problems, $u''+\lambda a(t) f(v) = 0$, $v''+\lambda b(t) g(u) = 0$, for $0 t 1$, and satisfying, $u(0) = \beta u(\eta)$, $u(1)=\alpha u(\eta)$, $v(0) = \beta v(\eta)$, $v(1) = \alpha v(\eta)$. A Guo-Krasnosel'skii fixed point theorem is applied.
Classification : 34A34, 34B10, 34B18
Keywords: generalized three-point boundary value problem; system of differential equations; eigenvalue problem 
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Henderson, J.; Ntouyas, S. K.; Purnaras, I. K. Positive solutions for systems of generalized three-point nonlinear boundary value problems. Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 1, pp. 79-91. http://geodesic.mathdoc.fr/item/CMUC_2008__49_1_a7/