In this paper, we are concerned with the existence of periodic solutions for a class of damped vibration problems. By introducing some new kinds of superquadratic and asymptotically quadratic conditions, and making use of the generalized mountain pass theorem in critical point theory, we propose a unified approach when the potential function exhibits either an asymptotically quadratic or a superquadratic behavior at infinity, and establish some sufficient conditions on periodic solutions, which extend and improve some recent results in the literature, even without damped vibration term.
Nous nous intéressons ici à l'existence de solutions périodiques pour une classe de problèmes de vibration amortie. Nous introduisons de nouvelles conditions de quadraticité asymptotique et de super-quadraticité, et nous utilisons un théorème du col généralisé de la théorie des points critiques. Ainsi, nous proposons une approche unifiée lorsque la fonction potentiel présente un comportement quadratique asymptotique ou super-quadratique à l'infini, et nous établissons des conditions suffisantes pour l'existence de solutions périodiques, ce qui étend et améliore plusieurs résultats récents, même en l'absence du terme de vibration amortie.
Accepted:
Published online:
Zhiyong Wang 1; Jihui Zhang 2
@article{CRMATH_2018__356_6_597_0,
author = {Zhiyong Wang and Jihui Zhang},
title = {Existence of periodic solutions for a class of damped vibration problems},
journal = {Comptes Rendus. Math\'ematique},
pages = {597--612},
publisher = {Elsevier},
volume = {356},
number = {6},
year = {2018},
doi = {10.1016/j.crma.2018.04.014},
language = {en},
}
Zhiyong Wang; Jihui Zhang. Existence of periodic solutions for a class of damped vibration problems. Comptes Rendus. Mathématique, Volume 356 (2018) no. 6, pp. 597-612. doi : 10.1016/j.crma.2018.04.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.04.014/
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