Uniqueness criterion for solutions of nonlocal problems on a finite interval for abstract singular equations
type: Item
instance of: scholarly article
title: Uniqueness criterion for solutions of nonlocal problems on a finite interval for abstract singular equations
zbMATH Open document ID: 1500.34053
DOI: 10.1134/S0001434622010047
author: A. V. Glushak
published in: Mathematical Notes
publication date: 2022-03-14T00:00:00Z
review text: Let \(E\) be a complex Banach space and let \(A,B\) be linear closed operators on \(E\) whose domains are not necessary dense. Consider the equation \[ B(u''(t)+\frac{k}{t}u'(t))=Au(t),\quad 0<t<1. \] The following cases are considered \begin{itemize} \item \(k\geq0\) with Neumann boundary condition \(u'(0)=0\) and non-local condition \(\int_0^1t^k(1-t^2)^{\alpha-1}u(t)dt=0\) (\(\alpha>0\)) \item \(k<1\) with Dirichlet boundary condition \(u(0)=0\) and non-local condition \(\int_0^1t(1-t^2)^{\beta-1}u(t)dt=0\) (\(\beta>0\)) \item \(k\geq0\) with Neumann boundary condition \(u'(0)=0\) and non-local condition \(a\int_0^1t^ku(t)dt+bu'(1)=0\) (\(a,b\ne0\)) \item \(k<1\) with Dirichlet boundary condition \(u(0)=0\) and non-local condition \(a\int_0^1t^ku(t)dt+b\lim_{t\to1}(t^{k-1}u(t))'=0\) \end{itemize} For each case a uniqueness criterion is established. Applications to the equation \(t^\gamma v''+bt^{\gamma-1}v'=Av\) are given.
reviewed by: Nikita V. Artamonov
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B16
zbMATH DE Number: 7488476
zbMATH Keywords: nonlocal problem
zbMATH Keywords: degenerate equation
zbMATH Keywords: uniqueness criterion
MaRDI profile type: Publication
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full work available at URL: s0001434622010047
OpenAlex ID: W4213436795
description: scientific article; zbMATH DE number 7488476