Geodesic
Singular systems of differential equations in Banach spaces
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 224 (2023), pp. 150-160

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Degenerate linear systems of differential equations of a special form in Banach spaces are considered. The structure of the solution of the Cauchy problem for such systems is completely determined by the properties of the matrix and operator pencils of the system. Solutions are constructed in the space of distributions with support bounded on the left and are restored using the matrix fundamental operator function of the system. Based on the analysis of the generalized solution constructed in this way, one can obtain theorems on the solvability in the space of functions of finite smoothness of the original Cauchy problem.
Keywords: Banach space, Fredholm operator, generalized function, fundamental matrix operator-function
Mots-clés : sheaf of constant matrices. 
@article{INTO_2023_224_a17,
     author = {M. V. Falaleev},
     title = {Singular systems of differential equations 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 = {150--160},
     publisher = {mathdoc},
     volume = {224},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_224_a17/}
}
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M. V. Falaleev. Singular systems of differential equations in Banach spaces. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 224 (2023), pp. 150-160. http://geodesic.mathdoc.fr/item/INTO_2023_224_a17/