Positive and Monotone Solutions of an m-point Boundary Value Problem
MetadataShow full metadata
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.
This work is licensed under a Creative Commons Attribution 4.0 International License.