Existence of solutions for a two point boundary value problem
type: Item
instance of: scholarly article
title: Existence of solutions for a two point boundary value problem
zbMATH Open document ID: 0608.34018
DOI: 10.1007/BF02844736
author: Bevan Thompson
publication date: 1986-01-01T00:00:00Z
review text: We consider the two point boundary value problem \(F[y]=y''-f(x,y,y')=0\), \(a\leq x\leq b\), \(y(a)=A\), \(y(b)=B\). Assuming that f satisfies certain differential inequalities associated with the existence of F-subfunctions and F-superfunctions, and that f also satisfies a suitable growth condition with respect to y', we prove that the two point boundary value problem has a solution y with (x,y(x),y'(x)) in a specified region; indeed we show that the problem has a maximal and a minimal solution in this region. Our results unify and generalize earlier results of K. Ako, L. K. Jackson, M. Nagumo, and others.
Mathematics Subject Classification ID: 34B10
zbMATH DE Number: 3983636
zbMATH Keywords: maximal solution
zbMATH Keywords: second order differential equation
zbMATH Keywords: two point boundary value problem
zbMATH Keywords: minimal solution
MaRDI profile type: Publication
cites work: Q5509200
cites work: Q5544507
cites work: Q5618592
cites work: An introduction to nonlinear boundary value problems
cites work: Q5330830
cites work: Subfunction and second-order ordinary differential inequalities
cites work: Q5768796
full work available at URL: https://doi.org/10.1007/bf02844736
OpenAlex ID: W2080340363
published in: Rendiconti del Circolo Matematico di Palermo
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description: scientific article; zbMATH DE number 3983636