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2007 Second-order integrodifferential equation with nonautonomous operators
D. Bahuguna, D. N. Pandey, A. Ujlayan
Differential Integral Equations 20(6): 681-692 (2007).

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.

Citation

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D. Bahuguna. D. N. Pandey. A. Ujlayan. "Second-order integrodifferential equation with nonautonomous operators." Differential Integral Equations 20 (6) 681 - 692, 2007.

Information

Published: 2007
First available in Project Euclid: 20 December 2012

zbMATH: 1210.45011
MathSciNet: MR2323044

Subjects:
Primary: 45N05
Secondary: 34A12, 34K30, 35L15, 35L90, 47G20, 47N20

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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Vol.20 • No. 6 • 2007
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