Abstract
We consider systems of second-order, quasilinear, ordinary differential equations with an identically degenerate matrix coefficient of the principal term and with well-posed initial conditions. Fundamental differences between such problems and systems of ordinary differential equations solved with respect to the second derivative are indicated. In terms of matrix polynomials, we formulate conditions of the existence and uniqueness of solutions of such problems in a neighborhood of the starting point.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 172, Proceedings of the Voronezh Winter Mathematical School “Modern Methods of Function Theory and Related Problems,” Voronezh, January 28 – February 2, 2019. Part 3, 2019.
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Bulatov, M.V., Solovarova, L.S. On a Certain Class of Quasilinear Second-Order Differential-Algebraic Equations. J Math Sci 268, 15–23 (2022). https://doi.org/10.1007/s10958-022-06176-1
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DOI: https://doi.org/10.1007/s10958-022-06176-1