Functions with Average and Bounded Motions of a Forced Discontinuous Oscillator

Abstract

In this paper we prove the existence of bounded solutions in the real line for the equation \(\ddot{u} + \mathrm{sign}(u)=p(t)\), where p is a function with average. Some useful density results for the space of functions with zero average are also obtained.

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Correspondence to Rafael Ortega.

Additional information

To Professor George Sell, in memoriam.

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Enguiça, R., Ortega, R. Functions with Average and Bounded Motions of a Forced Discontinuous Oscillator. J Dyn Diff Equat 31, 1185–1198 (2019). https://doi.org/10.1007/s10884-017-9595-1

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Keywords

  • Forced oscillator
  • Landesman–Lazer condition
  • Generating functions
  • Twist maps
  • Functions with average