Singular Hamiltonian elliptic systems with critical exponential growth in dimension two

We will focus on the existence of nontrivial solutions to the following Hamiltonian elliptic system− Δ u + V ( x ) u =g ( v )| x | a,x ∈ R 2 ,− Δ v + V ( x ) v =f ( u )| x | b,x ∈ R 2 ,where a , b are numbers belonging to the interval [0, 2), V is a continuous potential bounded below on R 2 by a positive constant and the functions f and g possess exponential growth range established by Trudinger–Moser inequalities in Lorentz–Sobolev spaces. The proof involves linking theorem and a finite‐dimensional approximation.