Positive and Monotone Solutions of an m-point Boundary Value Problem
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We 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.
CitationPalamides, P. K. (2002). Positive and monotone solutions of an m-point boundary value problem. Electronic Journal of Differential Equations, 2002(18), pp. 1-16.
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