Hamiltonian elliptic systems in dimension two with arbitrary and double exponential growth conditions.

In this paper we deal with the following class of Hamiltonian elliptic systems {−Δu = g(v) in Ω, −Δv = ƒ(u) in Ω, u = v = 0 on ∂Ω, where Ω ⊂ R² is a bounded domain and g is a nonlinearity with exponential growth condition. We derive the maximal growth conditions allowed for ƒ, proving that it can be of exponential type, double-exponential type, or completely arbitrary, depending on the conditions required for g. Under the hypothesis of arbitrary growth conditions or else when ƒ has a double exponential growth, we prove existence of nontrivial solutions for the system. [ABSTRACT FROM AUTHOR]