Lyapunov stability for regular equations and applications to the Liebau phenomenon Article Swipe

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stability (learning theory) mathematics kolmogorov–arnold–moser theorem twist lyapunov stability order (exchange) mathematical analysis type (biology) liénard equation applied mathematics hamiltonian system differential equation physics computer science geometry nonlinear system differential algebraic equation ordinary differential equation quantum mechanics economics ecology finance machine learning biology

Feng Wang , José Ángel Cid , Mirosława Zima , Mirosława Zima , ,Department of Mathematics, Nanjing University, Nanjing 210093, China , ,Departamento de Matemáticas, Universidade de Vigo, 32004, Pabellón 3, Campus de Ourense, Spain , ,Department of Functional Analysis, Faculty of Mathematics and Natural Sciences, University of Rzeszów, Pigonia 1, 35-959 Rzeszów, Poland ·

YOU? · · 2018 · Open Access · · DOI: https://doi.org/10.3934/dcds.2018204 · OA: W2809421136

We study the existence and stability of periodic solutions of two kinds of regular equations by means of classical topological techniques like the Kolmogorov-Arnold-Moser (KAM) theory, the Moser twist theorem, the averaging method and the method of upper and lower solutions in the reversed order. As an application, we present some results on the existence and stability of $ T$-periodic solutions of a Liebau-type equation.