The Cauchy problem for a degenerate operator-differential system of a special form in Banach spaces

In this paper, a degenerate operator-differential system of a special form in Banach spaces is examined. For this problem, it is necessary to take into account both the structure of the operator pencil and the matrix pencil; this is possible due to the notion of the matrix fundamental operator-valued function. Matrix fundamental operator-valued functions are constructed for the degenerate differential operator considered in the Fredholm and Noether cases. Also, formulas for generalized solutions of the corresponding Cauchy problems are obtained.