A priori estimates and solvability of problems with nonlinear functional boundary conditions
type: Item
instance of: scholarly article
zbMATH Open document ID: 0974.34011
publication date: 2001-12-04T00:00:00Z
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34K10
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 1577611
zbMATH Keywords: boundary value problem
zbMATH Keywords: functional boundary solution
zbMATH Keywords: a priori estimates
author: Sergei A. Brykalov
MaRDI profile type: Publication
title: A priori estimates and solvability of problems with nonlinear functional boundary conditions
published in: Differential Equations
review text: The author studies the solvability of the boundary value problem NEWLINE\[NEWLINEx^{(m)}(t)=F(x(\cdot))(t),\qquad t\in [a,b], \tag{1}NEWLINE\]NEWLINE with the nonlinear functional boundary conditions NEWLINE\[NEWLINEB^{k}_{i}(x^{(k)}_{i}(\cdot), x(\cdot))=0. \tag{2} NEWLINE\]NEWLINE The author obtains results that permit one to use a priori estimates for proving the solvability of problems with boundary conditions of a complicated structure and shows that if an a priori estimate holds, then there exists a solution.
description: scientific article