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arXiv · 2610.29496

The minimal period solution of Hamiltonian systems with even potentials

Huagui Duan·Yan Wu
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Abstract

We consider the autonomous system $\ddot{q}+\nabla V(q)=0$ 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.

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Huagui Duan, Yan Wu. 2026-10-21. The minimal period solution of Hamiltonian systems with even potentials. https://arxiv.org/abs/2610.29496

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