Subharmonic solutions of first order Hamiltonian systems with subquadratic condition

TL;DR

This paper proves the existence of subharmonic solutions in certain sub-quadratic Hamiltonian systems using variational methods and Maslov index theory, and also investigates minimal period problems.

Contribution

It introduces a novel approach combining homologically link theorem and Maslov index inequalities to establish subharmonic solutions and minimal period results.

Findings

Established existence of subharmonic solutions for sub-quadratic Hamiltonian systems.

Applied variational methods and Maslov index theory in the analysis.

Provided results on minimal period problems for autonomous systems.

Abstract

Using a homologically link theorem in variational theory and iteration inequalities of Maslov-type index, we prove the existences of a sequence of subharmonic solutions for one type of sub-quadratic non-autonomous Hamiltonian systems. Moreover, we also study the minimal period problem of some autonomous Hamiltonian systems with sub-quadratic condition.