Degenerate Integrodifferential Equations of Volterra Type in Banach Space

Abstract

This paper is concerned with the following degenerate integrodifferential equations of parabolic type.

$$ \left\{ {\begin{array}{*{20}{c}} {\frac{d}{{dt}}\left( {M\left( t \right)u\left( t \right)} \right) + L\left( t \right)u\left( t \right) + \int_{0}^{t} {K\left( {t,s} \right)u\left( s \right)ds = f\left( t \right),0 < t \leqslant T,} } \\ {M(t)u(t){|_{{t = 0}}} = M(0){u_{0}}.} \\ \end{array} } \right. $$

((1))