Lyapunov– Krasovsky Functionals and Partial Ultimate Equiboundedness of Solutions with Partial Control of Prehistories
This work was supported by the Russian Science Foundation grant № 25-21-00830
DOI:
https://doi.org/10.52575/2687-0959-2026-58-3-217-225Keywords:
Functional Differential Equation, Ultimate Equiboundedness of Solutions, Lyapunov– Krasovsky functionalAbstract
For solutions of functional differential equations of delay type, the concepts of equiboundedness of solutions, partial equiboundedness of solutions with partial control of their prehistories, ultimate equiboundedness of solutions, and partial ultimate equiboundedness of solutions with partial control of their prehistories are introduced. Using Lyapunov-Krasovsky functionals, sufficient conditions for the above-mentioned types of equiboundedness of solutions and ultimate equiboundedness of solutions are obtained. The results obtained can be used to analyze the behavior of solutions of complex retarded functional differential equations in various problems in the qualitative theory of differential equations, theoretical mechanics, and mathematical physics.
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