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Forced oscillations of a massive point on a compact surface with a boundary. (English) Zbl 1372.70023
Summary: We present sufficient conditions for the existence of a periodic solution for a class of systems describing the periodically forced motion of a massive point on a compact surface with a boundary.

70E18 Motion of a rigid body in contact with a solid surface
34C40 Ordinary differential equations and systems on manifolds
70F40 Problems involving a system of particles with friction
Full Text: DOI arXiv
[1] Benci, V.; Degiovanni, M., Periodic solutions of dissipative dynamical systems, (Variational Methods, (1990), Springer), 395-411
[2] Courant, R.; Robbins, H., What is mathematics?: an elementary approach to ideas and methods, (1941), Oxford University Press · JFM 67.0967.01
[3] Furi, M.; Pera, M. P., The forced spherical pendulum does have forced oscillations, (Delay Differential Equations and Dynamical Systems, (1991), Springer), 176-182 · Zbl 0736.34031
[4] Hamel, G., Über erzwungene schwingungen bei endlichen amplituden, (Festschrift David Hilbert zu Seinem Sechzigsten Geburtstag am 23. Januar 1922, (1922), Springer), 326-338 · JFM 48.0519.03
[5] Mawhin, J., Global results for the forced pendulum equation, (Handbook of Differential Equations: Ordinary Differential Equations, Vol. 1, (2000)), 533-589 · Zbl 1091.34019
[6] Polekhin, I. Y., Examples of topological approach to the problem of inverted pendulum with moving pivot point, Nelineinaya Din. [Russ. J. Nonlinear Dyn.], 10, 4, 465-472, (2014) · Zbl 1353.70051
[7] Srzednicki, R.; Wójcik, K.; Zgliczyński, P., Fixed point results based on the ważewski method, (Handbook of Topological Fixed Point Theory, (2005), Springer), 905-943 · Zbl 1079.37012
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