and Applied Analysis 3 B∞ There is h ∈ C Ω,R such that ∣∣f x, z ∣∣ ≤ h x , ∀ x, z ∈ Ω × R2, ∣∣g x, z ∣∣ ≤ h x , ∀ x, z ∈ Ω × R2. 1.8 Under these hypotheses, system 1.1 is asymptotically quadratic at infinity due to the presence of a linear part given by the function A ∈ S2 Ω . In addition, when λk A 1 for some k ≥ 1 the problem 1.1 becomes resonant. In this case, in order to obtain existence an...