Invariance of solutions of the set of regularized equations

Authors

  • A.A. Martynyuk S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kiev

DOI:

https://doi.org/10.15407/dopovidi2017.12.003

Keywords:

Eulerian solutions, set of uncertain equations, strict and weak invariances

Abstract

We consider the initial problem for a family of equations regularized with respect to the inaccuracy parameter. Definitions of the weak and strict invariances of solutions are introduced. The conditions for weak and strict invariances of the set of Euler solutions are established, and the possibility to consider discontinuous families of equations is indicated.

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References

Martynyuk, A. A. & Martynyuk-Chernienko, Yu. A. (2013). Existence, uniqueness, and estimation of solutions of the set of equations of perturbed motion. Ukr. Math. Journal. 65, No. 2, pp. 273-295 (in Russian). https://doi.org/10.1007/s11253-013-0779-5

Lakshmikantham, V. & Tolstonogov, A. (2003). Existence and interrelation between set and fuzzy differential equations. Nonlinear Analysis: TMA. No. 55, pp. 255-268. https://doi.org/10.1016/S0362-546X(03)00228-1

Lakshmikantham, V., Leela, S. & Martynyuk, A. A. (1989). Stability Analysis of Nonlinear Systems. New York: Marcel Dekker.

Bhaskar, G. T. & Lakshmikantham, V. (2003). Set differential equation and flow invariance Appl. Anal. No. 82, pp. 357-368.

Filippov, A. F. (1985). Differential equations with discontinuous right-hand side. Moscow: Nauka (in Russian).

Published

23.09.2024

How to Cite

Martynyuk, A. (2024). Invariance of solutions of the set of regularized equations . Reports of the National Academy of Sciences of Ukraine, (12), 3–7. https://doi.org/10.15407/dopovidi2017.12.003

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