Note to the Lagrange stability of excited pendulum type equations
Ján Andres, Staněk, Svatoslav (1993)
Mathematica Slovaca
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Displaying similar documents to “Nonlinear differential systems of the third and fourth order”
Note to the Lagrange stability of excited pendulum type equations
The Lyapunov stability for the linear and nonlinear damped oscillator with time-periodic parameters.
Chu, Jifeng, Xia, Ting (2010)
Abstract and Applied Analysis
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Integral manifolds and nonlinear oscillations
Hale, Jack K.
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On Lyapunov stability/instability of equilibria of free damped pendulum with periodically oscillating suspension point
Jiří Šremr (2025)
Applications of Mathematics
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We discuss Lyapunov stability/instability of both lower and upper equilibria of free damped pendulum with periodically oscillating suspension point. We recall the results of Bogolyubov and Kapitza, provide new effective criteria of stability/instability of the equilibria of pendulum equation, and give the exact and complete proofs. The criteria obtained are formulated in terms of positivity/negativity of Green's functions of the periodic boundary value problems for linearized equations....
Stability, Boundedness and Existenceof Periodic Solutions to Certain Third Order Nonlinear Differential Equations
A. T. ADEMOLA, M. O. OGUNDIRAN, P. O. ARAWOMO (2015)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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In this paper, criteria are established for uniform stability, uniform ultimate boundedness and existence of periodic solutions for third order nonlinear ordinary differential equations. In the investigation Lyapunov’s second method is used by constructing a complete Lyapunov function to obtain our results. The results obtained in this investigation complement and extend many existing results in the literature.