On a class of Hamiltonian elliptic systems involving unbounded or decaying potentials in dimension two (Q2832670)

In this paper, the authors consider the following class of Hamiltonian elliptic systems NEWLINE\[NEWLINE\begin{cases} -\Delta u+V(x)u= H_v(x,u,v),\quad x\in\mathbb R^2,\\ -\Delta v+V(x)v= H_u(x,u,v),\quad x\in\mathbb R^2.\end{cases}\leqno{(1)}NEWLINE\]NEWLINE Under some suitable conditions on the potential \(V\) and the Hamiltonian \(H(x,u,v),\) using an approximation argument and a version of the Trudinger-Moser inequality, the authors establish the existence of positive solutions to problem (1).