Second-order integrodifferential equation with nonautonomous operators
| Autor: | D. Bahuguna, D. N. Pandey, A. Ujlayan |
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| Jazyk: | angličtina |
| Rok vydání: | 2007 |
| Předmět: | |
| Zdroj: | Differential Integral Equations 20, no. 6 (2007), 681-692 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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