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Keywords:
generalized three-point boundary value problem; system of differential equations; eigenvalue problem
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.
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