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Global Solvability of Time-Varying Semilinear Differential-Algebraic Equations, Boundedness and Stability of Their Solutions. I

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Abstract

For time-varying semilinear differential-algebraic equations, we prove theorems on the existence and uniqueness of global solutions and theorems on Lagrange stability (boundedness of global solutions), dissipativity (ultimate boundedness of solutions), and Lagrange instability (absence of global solutions).

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Funding

This study was supported by the National Academy of Sciences of Ukraine (project “Qualitative, asymptotic, and numerical analysis of various classes of differential equations and dynamical systems, their classification and practical application,” state reg. no. 0119U102376).

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Authors and Affiliations

  1. B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Kharkiv, 61103, Ukraine

    M. S. Filipkovskaya

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  1. M. S. Filipkovskaya
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Correspondence to M. S. Filipkovskaya.

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Translated by V. Potapchouck

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Filipkovskaya, M.S. Global Solvability of Time-Varying Semilinear Differential-Algebraic Equations, Boundedness and Stability of Their Solutions. I. Diff Equat 57, 19–40 (2021). https://doi.org/10.1134/S0012266121010031

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  • DOI: https://doi.org/10.1134/S0012266121010031

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