English

Bounded solutions for a forced bounded oscillator without friction

Classical Analysis and ODEs 2014-02-18 v1 Analysis of PDEs

Abstract

Under the validity of a Landesman-Lazer type condition, we prove the existence of solutions bounded on the real line, together with their first derivatives, for some second order nonlinear differential equation of the form u¨+g(u)=p(t)\ddot u + g(u) = p(t), where the reaction term gg is bounded. The proof is variational, and relies on a dual version of the Nehari method for the existence of oscillating solutions to superlinear equations.

Keywords

Cite

@article{arxiv.1306.0797,
  title  = {Bounded solutions for a forced bounded oscillator without friction},
  author = {Nicola Soave and Gianmaria Verzini},
  journal= {arXiv preprint arXiv:1306.0797},
  year   = {2014}
}
R2 v1 2026-06-22T00:27:49.810Z