On a Singular Class of Hamiltonian Systems in Dimension Two

Abstract

Let $\Omega$ be a bounded domain in ${\mathbb{R}}^2$. In this paper, we consider the following systems of semilinear elliptic equations

where $a,b\in [0,2)$ and the functions $f$ and $g$ are nonlinearities having an exponential growth on $\Omega$. This nonlinearity is motivated by suitable Trudinger-Moser inequality with a singular weight. In fact, we prove the existence of a nontrivial solution to (S). For the proof we use a variational argument (a linking theorem).