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Bounded solutions to a system of second order ODEs and the Whitney pendulum. (English) Zbl 1345.34045
Summary: We give an existence theorem for bounded solutions to a system of second order ODEs. Dynamical applications are considered.

MSC:
34C11 Growth and boundedness of solutions to ordinary differential equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
70H03 Lagrange’s equations
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[1] [1]V. Arnold, What is mathematics?, MCCME, Moscow, 2002 (in Russian).
[2] [2]R. Courant and H. Robbins, What is Mathematics? An Elementary Approach to Ideas and Methods, Oxford Univ. Press, 1996. · Zbl 0865.00001
[3] [3]I. Polekhin, Inverted pendulum with moving pivot point: examples of topological approach, arXiv:1407.4787 (2014). Whitney pendulum165 · Zbl 1353.70051
[4] [4]R. Srzednicki, K. W\'{}ojcik and P. Zgliczy\'{}nski, Fixed point results based on the Wa\dot{}zewski method, in: Handbook of Topological Fixed Point Theory, R. Brown et al. (eds.), Springer, 2005, 903–941.
[5] [5]T. Wa\dot{}zewski, Sur un principe topologique de l’examen de l’allure asymptotique des int\'{}egrales des \'{}equations diff\'{}erentielles ordinaires, Ann. Soc. Polon. Math. 20 (1947), 279–313.
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