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.
Authors
Additional information
- DOI
- Digital Object Identifier link open in new tab 10.3934/dcdss.2019121
- Category
- Publikacja w czasopiśmie
- Type
- artykuły w czasopismach
- Language
- angielski
- Publication year
- 2019
