Ultimate boundedness in the sense of Poisson of solutions to systems of differential equations and Lyapunov functions

DOI10.1134/S0001434618010236zbMath1394.34062OpenAlexW2792615782MaRDI QIDQ1646362

K. S. Lapin

Publication date: 25 June 2018

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434618010236

zbMATH Keywords

Lyapunov functionboundedness of solutionsboundedness of solutions in sense of Poissonpartial boundedness of solutionspartially controllable initial conditions

Mathematics Subject Classification ID

Stability of solutions to ordinary differential equations (34D20) Growth and boundedness of solutions to ordinary differential equations (34C11) Asymptotic properties of solutions to ordinary differential equations (34D05)

Related Items (7)

Examples of differential systems with contrasting combinations of Lyapunov, Perron, and upper-limit properties ⋮ Total Poisson boundedness of solutions of \(\mathcal{P}\)-perturbed complex systems of differential equations ⋮ Lyapunov vector functions, Krasnosel'skii canonical domains, and existence of Poisson bounded solutions ⋮ Lyapunov functions, Krasnosel'skii canonical domains, and the existence of Poisson bounded solutions ⋮ Vector Lyapunov functions, complete sets of guiding functions, and the existence of Poisson bounded solutions ⋮ Higher Lyapunov functions derivatives and total Poisson boundedness of solutions ⋮ Guiding functional families, Lyapunov vector functions, and the existence of Poisson bounded solutions

Cites Work

• On partial stability theory of nonlinear dynamic systems
• Ultimate boundedness with respect to part of the variables of solutions of systems of differential equations with partly controlled initial conditions
• Partial uniform boundedness of solutions of systems of differential equations with partly controlled initial conditions
• Uniform boundedness in part of the variables of solutions to systems of differential equations with partially controllable initial conditions
• Stability in part of the variables of ``partial equilibria of systems with aftereffect
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