PreprintCC0arXiv
The minimal period solution of Hamiltonian systems with even potentials
Abstract
We consider the autonomous system q̈+∇ V(q)=0 in an arbitrary finite-dimensional Euclidean space. The potential is assumed to be even, nonnegative and of class C2, to satisfy V(x)=o(|x|2) at the origin, and the Ambrosetti--Rabinowitz superquadratic inequality outside a ball. We prove that, for every prescribed T>0, the system has a nonconstant solution with T being its minimal positive period.
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BibTeX
@misc{duan2026minimal,
title = {{The minimal period solution of Hamiltonian systems with even potentials}},
author = {Huagui Duan and Yan Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29496},
eprint = {2610.29496},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29496},
note = {CC0},
}
RIS
TY - UNPB
TI - The minimal period solution of Hamiltonian systems with even potentials
AU - Huagui Duan
AU - Yan Wu
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29496
UR - https://arxiv.org/abs/2610.29496
AB - We consider the autonomous system q̈+∇ V(q)=0 in an arbitrary finite-dimensional Euclidean space. The potential is assumed to be even, nonnegative and of class C^2, to satisfy V(x)=o(|x|^2) at the origin, and the Ambrosetti--Rabinowitz superquadratic inequality outside a ball. We prove that, for every prescribed T>0, the system has a nonconstant solution with T being its minimal positive period.
ER -