Differential and Integral Equations

Nonautonomous integro-differential equations of hyperbolic type

Hirokazu Oka and Naoki Tanaka

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


This paper is devoted to two problems for the nonautonomous integrodifferential equation in a Banach space $X$ of hyperbolic type $$ \text{$u'(t) = A(t)u(t)+ \int_0^t B(t,s)u(s) ds + f(t)$ for $t\in[0,T]$, and $u(0) = u_0$.} $$ One is the problem of existence and uniqueness of classical solutions without assuming that the common domain of $A(t)$ is dense in $X$, and the other is the regularity problem in the case where the common domain of $A(t)$ is dense in $X$. The regularity result will play a role in developing an abstract theory which can be applied to the second-order integrodifferential equations with the third kind boundary conditions.

Article information

Differential Integral Equations, Volume 8, Number 7 (1995), 1823-1831.

First available in Project Euclid: 12 May 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 45N05: Abstract integral equations, integral equations in abstract spaces
Secondary: 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx]


Oka, Hirokazu; Tanaka, Naoki. Nonautonomous integro-differential equations of hyperbolic type. Differential Integral Equations 8 (1995), no. 7, 1823--1831. https://projecteuclid.org/euclid.die/1368397760

Export citation