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Large time behavior of solutions to a system of coupled nonlinear oscillators via a generalized form of Schauder-Tychonoff fixed point theorem | |
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Fixed Point Theory, Volume 23, No. 2, 2022, 591-606, June 15th, 2022 DOI: 10.24193/fpt-ro.2022.2.11 Authors: Gheorghe Moroșanu and Cristian Vladimirescu Abstract: In this paper we investigate the stability of the null solution of a system of ODEs describing the motion of two coupled damped nonlinear oscillators. We also show that for any solution (x,y) of the system we have limt → +∞ x(t) = limt → +∞ẋ(t) =limt → +∞y(t) =limt → +∞ẏ(t) = 0, for small initial data in the case when the uniqueness of solutions is not guaranteed. Our proofs are mainly based on a generalized form of Schauder-Tychonoff fixed point theorem. The theoretical results are illustrated with numerical simulations. Key Words and Phrases: Coupled oscillators, uniform stability, asymptotic stability, fixed point theorem. 2010 Mathematics Subject Classification: 34D20, 47H10. Published on-line: June 15th, 2022.
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