Subharmonic solutions for a class of Lagrangian systems

Anouar Bahrouni; Marek Izydorek; Joanna Janczewska

doi:10.3934/dcdss.2019121

Subharmonic solutions for a class of Lagrangian systems

Abstract

We prove that second order Hamiltonian systems with a potential of class C1, periodic in time and superquadratic at infinity with respect to the space variable have subharmonic solutions. Our intention is to generalise a result on subharmonics for Hamiltonian systems with a potential satisfying the global Ambrosetti-Rabinowitz condition from [P. H. Rabinowitz, Proc. Roy. Soc. Edinburgh Sect. A, 114 (1990), 33-38]. Indeed, we weaken the latter condition in a neighbourhood of the origin. We will also discuss when subharmonics pass to a nontrivial homoclinic orbit.

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Authors (3)

Anouar Bahrouni
- Department of Mathematics, Faculty of Sciences University of Monastir 5019 Monastir, Tunisia
Marek Izydorek prof. dr hab.
Joanna Janczewska prof. dr hab.

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Articles

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artykuły w czasopismach

Published in:

Discrete and Continuous Dynamical Systems-Series S no. 12, pages 1841 - 1850,
ISSN: 1937-1632

Language:

English

Publication year:

2019

Bibliographic description:

Bahrouni A., Izydorek M., Janczewska J.: Subharmonic solutions for a class of Lagrangian systems// Discrete and Continuous Dynamical Systems-Series S -Vol. 12,iss. 7 (2019), s.1841-1850

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