Hamiltonian elliptic systems in dimension two with potentials which can vanish at infinity

Abstract

We will focus on the existence of nontrivial solutions to the following Hamiltonian elliptic system [Formula: see text] where [Formula: see text] is a positive function which can vanish at infinity and be unbounded from above and [Formula: see text] and [Formula: see text] have exponential growth range. The proof involves a truncation argument combined with the linking theorem and a finite-dimensional approximation.