Higher-order derivatives of Lyapunov functions and ultimate boundedness in the sense of Poisson of solutions to systems of differential equations

DOI10.1134/S0037446618060137zbMath1415.34065OpenAlexW2906122286MaRDI QIDQ1731402

K. S. Lapin

Publication date: 13 March 2019

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

Full work available at URL: https://doi.org/10.1134/s0037446618060137

zbMATH Keywords

Lyapunov functionpartially controlled initial conditionsequiultimate boundednesshigherorder derivativesuniform-ultimate boundedness

Mathematics Subject Classification ID

Growth and boundedness of solutions to ordinary differential equations (34C11)

Related Items (3)

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 ⋮ Guiding functional families, Lyapunov vector functions, and the existence of Poisson bounded solutions

Cites Work

• On bounded solutions of ordinary nonlinear differential equations of order \(n\)
• On the stability and boundedness of solutions of nonlinear vector differential equations of third order
• Ultimate boundedness of solutions for a generalized Liénard equation with forcing term
• Poisson total boundedness of solutions of systems of differential equations and Lyapunov vector functions
• Ultimate boundedness with respect to part of the variables of solutions of systems of differential equations with partly controlled initial conditions
• A note on boundedness of solutions to a class of non-autonomous differential equations of second order
• Solutions of systems of differential equations, bounded with respect to part of the variables
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