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Second-order integrodifferential equation with nonautonomous operators

Authors :
D. Bahuguna
D. N. Pandey
A. Ujlayan
Source :
Differential Integral Equations 20, no. 6 (2007), 681-692
Publication Year :
2007
Publisher :
Khayyam Publishing, Inc., 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.

Details

Language :
English
Database :
OpenAIRE
Journal :
Differential Integral Equations 20, no. 6 (2007), 681-692
Accession number :
edsair.doi.dedup.....b71981564c00412509eeeefe289473f5