Uniqueness and existence for perturbed focal boundary value problems
type: Item
instance of: scholarly article
title: Uniqueness and existence for perturbed focal boundary value problems
zbMATH Open document ID: 1097.34014
published in: Applied Mathematics Letters
publication date: 2006-01-24T00:00:00Z
review text: The author considers the existence and uniqueness of a solution to the equation \[ y^{(n)}=f(t, y, y',\dots, y^{(n-1)})\tag{1} \] satisfying the nonlinear boundary conditions \[ a_{ii}y(t_i)+a_{i,i+1}y'(t_i)+\dots+a_{i,n}y^{(n-1)}(t_i)+B_i(y(t_i), \dots, y^{(n-1)}(t_i))=y_i, \tag{2} \] \(i=1, 2, \dots, n\). Assume that for each solution of equation (1), the solution to the variational boundary value problem is unique. The author proves the existence and uniqueness of the solution to the boundary value problem (1), (2), which generalizes the focal boundary value problems.
reviewed by: Zaihong Wang
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B10
zbMATH DE Number: 5001484
zbMATH Keywords: focal boundary value problems
zbMATH Keywords: uniqueness
zbMATH Keywords: existence
zbMATH Keywords: variational equation
author: Jeffrey Ehme
MaRDI profile type: Publication
full work available at URL: j.aml.2004.10.004
OpenAlex ID: W2049759920
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DOI: 10.1016/J.AML.2004.10.004
description: scientific article; zbMATH DE number 5001484