Geodesic
The Cauchy problem for a degenerate operator-differential system of a special form in Banach spaces
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 196 (2021), pp. 105-113

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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.
Keywords: Banach space, Fredholm operator, generalized functions, matrix fundamental operator-valued function, regular matrix pencil. 
@article{INTO_2021_196_a9,
     author = {O. V. Slastnaya},
     title = {The {Cauchy} problem for a degenerate operator-differential system of a special form in {Banach} spaces},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {105--113},
     publisher = {mathdoc},
     volume = {196},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_196_a9/}
}
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O. V. Slastnaya. The Cauchy problem for a degenerate operator-differential system of a special form in Banach spaces. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 196 (2021), pp. 105-113. http://geodesic.mathdoc.fr/item/INTO_2021_196_a9/