Ground state solutions for Hamiltonian systems with double exponential growth

This study explores the existence of ground state solutions for a Hamiltonian elliptic system in the whole plane $\mathbb{R}^{2}$ , involving double exponential growth nonlinearities, which are given by the Trudinger–Moser inequalities in weighted radial Sobolev spaces. To find solutions, we apply a minimizing process on a generalized Nehari manifold.