In this paper we consider the problems of correct solvability of the initial value problem for a class of differential equations in Banach spaces. We apply the method of reduction of degenerate differential equation to the regular problems using the properties of the Jordan structure of the equation operator coefficients. The sufficient conditions for the correct solvability and stability as t rightarrow + infty of the initial value problem for the equations unsolved according to derivatives depending on the equation operator coefficients are obtained. The abstract theorems are used for statement and investigation of initial value problems for partial differential equation and integral equation.

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