Subharmonic solutions for nonautonomous sublinear first order Hamiltonian systems

TL;DR

This paper proves the existence of subharmonic solutions in non-autonomous first-order Hamiltonian systems using minimax methods and the least action principle, extending previous results and analyzing period minimality.

Contribution

It introduces new existence results for subharmonic solutions in non-autonomous Hamiltonian systems, improving upon prior findings with advanced critical point techniques.

Findings

Established existence of subharmonic solutions

Analyzed minimality of periods for solutions

Extended previous theoretical results

Abstract

In this paper, the existence of subharmonic solutions for a class of non-autonomous first-order Hamiltonian systems is investigated. We also study the minimality of periods for such solutions. Our results which extend and improve many previous results will be illustrated by specific examples. Our main tools are the minimax methods in critical point theory and the least action principle. {\bf Key words.} Hamiltonian systems. Critical point theory. Least action principle. Subharmonic solutions.