On a class of boundary value problems for singular equations
type: Item
instance of: scholarly article
title: On a class of boundary value problems for singular equations
zbMATH Open document ID: 0858.34053
author: A. V. Kungurtseva
published in: Russian Mathematics
publication date: 1996-09-01T00:00:00Z
review text: Under some conditions the boundary value problem \(Lx=Fx\), \(lx=\varphi x\) for the equation \(Lx=Fx\) has a solution. Here \(L:D\to B\) is a bounded linear operator, \(F:D\to B\) a continuous operator, \(l:D\to\mathbb{R}^n\) a bounded linear functional, \(\varphi:D\to\mathbb{R}^n\) a continuous functional, \(B\) and \(D\) are Banach spaces, whereby \(D\) is isomorphic to the direct product \(B\times\mathbb{R}^n\). The result is applied to the boundary value problem \(\psi(t)\ddot x(t)+\beta\dot x(t)=f(t,x(t))\), \(t\in [a,b]\), \(x(a)=\alpha_1\), \(x'(b)=\alpha_2\) representing a mathematical model of processes in chemical reactors.
Mathematics Subject Classification ID: 34K10
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47N60
zbMATH DE Number: 923034
zbMATH Keywords: boundary value problem
zbMATH Keywords: Banach spaces
zbMATH Keywords: mathematical model of processes in chemical reactors
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 923034