Palamides, Panos K.2020-07-132020-07-132002-02-18Palamides, P. K. (2002). Positive and monotone solutions of an m-point boundary value problem. <i>Electronic Journal of Differential Equations, 2002</i>(18), pp. 1-16.1072-6691https://hdl.handle.net/10877/12058We study the second-order ordinary differential equation y''(t) = -ƒ(t, y(t), y'(t)), 0 ≤ t ≤ 1, subject to the multi-point boundary conditions αy(0) ± βy' (0) = 0, y(1) = Σm-2i=1 αiy(ξi). We prove the existence of a positive solution (and monotone in some cases) under superlinear and/or sublinear growth rate in ƒ. Our approach is based on an analysis of the corresponding vector field on the (y, y') face-plane and on Kneser's property for the solution's funnel.Text16 pages1 file (.pdf)enAttribution 4.0 InternationalMultipoint boundary value problemsPositive monotone solutionVector fieldSublinearSuperlinearKneser's propertySolution's funelArticle