Differential and Integral Equations

Second-order integrodifferential equation with nonautonomous operators

D. Bahuguna, D. N. Pandey, and A. Ujlayan

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

Abstract

In this paper, we establish some results to show the existence and uniqueness of classical solution of the non-autonomous second-order integrodifferential equation of the type: \begin{eqnarray*} u''(t) & = & A(t)\;[u(t)+\int_0 ^{t} k_{1}(t,s)u(s)ds]'+B(t)\;[u(t)+\int_0 ^{t} k_{2}(t,s)u(s)ds]\\ & & +f(t),\; 0\leq t \leq T, \\ u(0) & = & u_{0} \in E,\quad u'(0)=u_{1} \in E, \end{eqnarray*} on a Banach space $E$, by means of the matrix operator method.

Article information

Source
Differential Integral Equations Volume 20, Number 6 (2007), 681-692.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356039432

Mathematical Reviews number (MathSciNet)
MR2323044

Zentralblatt MATH identifier
1210.45011

Subjects
Primary: 45N05: Abstract integral equations, integral equations in abstract spaces
Secondary: 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx] 35L15: Initial value problems for second-order hyperbolic equations 35L90: Abstract hyperbolic equations 47G20: Integro-differential operators [See also 34K30, 35R09, 35R10, 45Jxx, 45Kxx] 47N20: Applications to differential and integral equations

Citation

Bahuguna, D.; Pandey, D. N.; Ujlayan, A. Second-order integrodifferential equation with nonautonomous operators. Differential Integral Equations 20 (2007), no. 6, 681--692. https://projecteuclid.org/euclid.die/1356039432.


Export citation