Abstract: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.
Keywords: generalized three-point boundary value problem, system of differential equations, eigenvalue problem
AMS Subject Classification: 34B18, 34A34