Boundary value problems for second order differential equations of Sobolev type
type: Item
instance of: scholarly article
title: Boundary value problems for second order differential equations of Sobolev type
zbMATH Open document ID: 0657.34020
DOI: 10.1016/0898-1221(88)90080-6
publication date: 1988-01-01T00:00:00Z
review text: The author considers the boundary value problem of Sobolev type \[ u''(t,x)=f[t,x,u(t,x),u'(t,x)],\quad t,x\in J=[a,b], \] \[ u(a,x)=\alpha (x),\quad u(b,x)=\beta (x),\quad x\in J, \] where \(f\in C(J\times J\times R^ n\times R^ n,R^ n)\), \(\alpha,\beta \in C(J,R^ n)\). In particular, he provides necessary and sufficient conditions for the existence and uniqueness of a solution to this problem and sufficient conditions for the convergence of the Picard and approximate Picard methods to this solution.
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 4073459
zbMATH Keywords: Picard method
zbMATH Keywords: boundary value problem of Sobolev type
zbMATH Keywords: approximate Picard methods
author: Ravi P. Agarwal
reviewed by: Milan Tvrdý
MaRDI profile type: Publication
full work available at URL: 0898-1221(88)90080-6
OpenAlex ID: W2073968511
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4073459