Positive solutions for systems of generalized three-point nonlinear boundary value problems

summary: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