Periodic Bouncing Solutions for Nonlinear Impact Oscillators

Alessandro Fonda 1  and Andrea Sfecci 2
  • 1 Università degli Studi di Trieste P.le Europa 1, Trieste, I-34127 Italy
  • 2 SISSA - International School for Advanced Studies Via Bonomea 265, Trieste, I-34136 Italy

Abstract

We prove the existence of a periodic solution to a nonlinear impact oscillator, whose restoring force has an asymptotically linear behavior. To this aim, after regularizing the problem, we use phase-plane analysis, and apply the Poincaré-Bohl fixed point Theorem to the associated Poincaré 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.

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