Application of implicit function theorems to existence of solutions to ordinary differential equations with nonlocal boundary conditions
type: Item
instance of: scholarly article
title: Application of implicit function theorems to existence of solutions to ordinary differential equations with nonlocal boundary conditions
zbMATH Open document ID: 1028.34017
DOI: 10.1016/S0022-247X(02)00262-7
author: Yanyan Li
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-02-11T00:00:00Z
review text: The authors study classical solutions to the boundary value problem \[ y''= a(x,y)(y- b),\quad y(0)= 0,\quad y'(1)= g(y(\xi), y'(\xi)), \] where \(y(x)\) for \(0\leq x\leq 1\) is a scalar unknown function, the functions \(a\), \(g\) and numbers \(b\), \(\xi\) are given. This nonlocal problem models steady-state temperature distributions along a rod when the heat flux at the end \(x= 1\) is regulated depending on the observation of the temperature and of the heat flux at some interior point \(\xi\). Sufficient conditions are given for the existence, uniqueness, and positivity of solutions. Some lemmas proved by the authors have the form of implicit function theorems.
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 80A20
Mathematics Subject Classification ID: 26B10
zbMATH DE Number: 1866581
zbMATH Keywords: second-order boundary value problems
zbMATH Keywords: nonlocal boundary conditions
zbMATH Keywords: steady-state heat conduction
zbMATH Keywords: implicit function theorems
reviewed by: Sergei A. Brykalov
MaRDI profile type: Publication
cites work: Q4253594
cites work: On the existence of solutions for a class of first-order differential equations
cites work: Boundary value problems for nonlinear ordinary differential equations
cites work: Q3149682
cites work: Nonlinear boundary value problems for some classes of ordinary differential equations
cites work: Some general existence principles in the Carathéodory theory of nonlinear differential systems
cites work: Three‐Point Boundary Value Problems in Differential Equations
cites work: Existence results for some \(n\)-dimensional nonlocal boundary value problems
cites work: Q3769207
cites work: Q3202429
cites work: On a nonlocal boundary value problem for second order linear ordinary differential equations
cites work: Three-point boundary value problem for nonlinear second-order differential equation with parameter
cites work: Q4882889
description: scientific article; zbMATH DE number 1866581