We prove the existence of a periodic solution to a nonlinear impact oscillator, whose restor- ing force has an asymptotically linear behavior. To this aim, after regularizing the problem, we use phase-plane analysis, and apply the Poincare ́–Bohl fixed point Theorem to the as- sociated Poincare ́ map, so to find a periodic solution of the regularized problem. Passing to the limit, we eventually find the “bouncing solution” we are looking for.

Periodic bouncing solutions for nonlinear impact oscillators / Fonda, Alessandro; Sfecci, Andrea. - In: ADVANCED NONLINEAR STUDIES. - ISSN 1536-1365. - STAMPA. - 13:1(2013), pp. 179-189. [10.1515/ans-2013-0110]

Periodic bouncing solutions for nonlinear impact oscillators

SFECCI, Andrea
2013-01-01

Abstract

We prove the existence of a periodic solution to a nonlinear impact oscillator, whose restor- ing force has an asymptotically linear behavior. To this aim, after regularizing the problem, we use phase-plane analysis, and apply the Poincare ́–Bohl fixed point Theorem to the as- sociated Poincare ́ map, so to find a periodic solution of the regularized problem. Passing to the limit, we eventually find the “bouncing solution” we are looking for.
2013
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/251305
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