Some progress on minimal period problems in reversible semi-positive Hamiltonian systems

Abstract

In this paper, we study the minimal period problems in superquadratic and asymptotically linear reversible semi-positive Hamiltonian systems in R2n, respectively. We show that for every T>0, there exists a T-periodic brake orbit with minimal period not less than T/(n+1) for both cases, which is an extension of the results in [55] and [20].