On periodic Hamiltonian elliptic systems with spectrum point zero

Abstract

In this paper, we study the existence and multiplicity of solutions for a class of periodic Hamiltonian elliptic systems with spectrum point zero. By applying two recent critical point theorems for strongly indefinite functionals, we present some new criteria to guarantee that Hamiltonian elliptic systems with spectrum point zero have a ground state solution and infinitely many geometrically distinct solutions when the potential satisfies the asymptotically quadratic and weak superquadratic conditions, respectively. Some recent results are extended and improved.