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We reduce the problem with some history prescribed for an integrodifferential equation in a Banach space including memory effect to the Cauchy problem for some evolution system with a constant operator in a larger space that possesses a resolvent (C0)-semigroup. This enables us to state conditions for the existence of a unique classical solution to the original problem. We use the results...
We establish sufficient conditions of the local and global solvability of initial value problems for a class of linear operator-differential equations of the first order in a Banach space. Equations are assumed to have a degenerate operator at the derivative and an integral delay operator. We apply methods of the theory of degenerate semigroups of operators and the contraction mapping theorem. As...
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