Positive and Monotone Solutions of an m-point Boundary Value Problem
Date
2002-02-18
Authors
Palamides, Panos K.
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
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.
Description
Keywords
Multipoint boundary value problems, Positive monotone solution, Vector field, Sublinear, Superlinear, Kneser's property, Solution's funel
Citation
Palamides, 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.
Rights
Attribution 4.0 International