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 , where the reaction term 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.
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}
}