Generalized two point boundary value problems. Existence and uniqueness
type: Item
instance of: scholarly article
title: Generalized two point boundary value problems. Existence and uniqueness
zbMATH Open document ID: 0759.34016
DOI: 10.1155/S1048953392000121
author: K. N. Murty
author: Seenith Sivasundaram
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 1993-01-16T00:00:00Z
full work available at URL: https://eudml.org/doc/46768
review text: The boundary value problem \(P(t)y'+Q(t)y=f(t)\), \(a\leq t\leq b\), \(My(a)+Ny(b)=d\) where \(P,Q\in[L_ p(a,b)]^{m\times n}\), \(f\in[L_ p(a,b)]^ n\) for some \(p\), \(1\leq p\leq\infty\); \(M,N\in R^{n\times m}\), \(d\in R^ n\), is considered. If this problem is non invertible an algorithm is presented for finding the pseudo-inverse of a rectangular matrix. Using these pseudo-inverses existence and uniqueness of solutions are established. The case of multipoint boundary value problem is considered too. Two illustrative examples are given.
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B27
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 94154
zbMATH Keywords: boundary value problem
zbMATH Keywords: algorithm
zbMATH Keywords: pseudo-inverse
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: multipoint boundary value problem
zbMATH Keywords: examples
reviewed by: Josef Diblík
MaRDI profile type: Publication
OpenAlex ID: W2021539420
description: scientific article; zbMATH DE number 94154