Subharmonics of a Nonconvex Noncoercive Hamiltonian System

Abstract

We study the problem of the existence of multiple periodic solutions of the Hamiltonian system $$J\dot x + u\nabla G\left( {t,u\left( x \right)} \right) = e\left( t \right),$$ where u is a linear mapping, G is a C ¹-function, and e is a continuous function.