Special Issue in honor of Alan C. Lazer. Electron. J. Diff. Eqns., Special Issue 01 (2021), pp. 203-212.

Remarks on periodic resonant problems with nonlinear dissipation

Luis Sanchez, Joao G. Silva

Abstract:
We consider the periodic problem for a 2nd order ODE with non-invertible linear part, and mild nonlinear dissipation term. The motivation for this study is a paper by Lazer [9] We add a bounded restoring force g(u) and show that the sufficient condition (of Landesman-Lazer type) given in [9] still implies the existence of a periodic solution in our case. We also comment on some variants of the problem and on the existence of bounded solutions.

Published October 6, 2021.
Math Subject Classifications: 34B15, 34C11, 34C25.
Key Words: Periodic solution; resonance; bounded solution.
DOI: https://doi.org/10.58997/ejde.sp.01.s1

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Luís Sanchez
CMAFcIO
Faculdade de Ciências da Universidade de Lisboa
Campo Grande 1749-016 Lisboa, Portugal
email: lfrodrigues@ciencias.ulisboa.pt
João G. Silva
Faculdade de Ciências da Universidade de Lisboa
Campo Grande 1749-016 Lisboa, Portugal
email: jgs1891@outlook.com

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