On a generalized integro-differential equation of Barbashin type
type: Item
instance of: scholarly article
title: On a generalized integro-differential equation of Barbashin type
zbMATH Open document ID: 0842.45008
DOI: 10.4171/ZAA/656
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1996-07-24T00:00:00Z
review text: The main goal of this paper is to consider the following integro-differential equation: \[ \begin{multlined} {{\partial u (t, \tau, s)} \over {\partial \tau}}= C(t, \tau, s) u(t, \tau, s) + \int^b_a C(t, \tau, s, \sigma) u(t, \tau, \sigma)d\sigma\\+ \int^b_a m(t, \tau, s, r)u (r, \tau, s)dr+ \int^b_a \int^b_a n(t, \tau, s, \sigma, r) u(r, \tau, \sigma) d\sigma dr+ f(t, \tau, s) \end{multlined} \tag{1} \] and the operator differential equation \[ {{du (\tau)} \over {d\tau}}= A(\tau) u(\tau)+ f(\tau) \qquad (\tau\in J), \tag{2} \] where \(A(\tau)= C(\tau) K(\tau)\), \(K(\tau)= L(\tau)+ M(\tau)+ N(\tau)\), with \(C(\tau) u(t, s)= C(t, \tau, s) u(t,s)\), \(L(\tau) u(t,s)= \int^b_a L(t, \tau, s, \sigma) u(t, \sigma) d\sigma\), \(M(\tau) u(t,s)= \int^b_a m(t, \tau, s, r) u(r, s)dr\), \(N(\tau) u(t,s)= \int^b_a \int^b_a n(t, \tau, s, \sigma, r) u(r, \sigma) d\sigma dr\). The author studies the solution of (1) by means of the investigation of equation (2) and obtains some results. Moreover, he discusses a corresponding generalized boundary value problem.
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 34G10
zbMATH DE Number: 856799
zbMATH Keywords: generalized integro-differential equation of Barbashin type
zbMATH Keywords: operator differential equation
zbMATH Keywords: boundary value problem
Wikidata QID: Q115211687
author: Chur-Jen Chen
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 856799