The Ambrosetti–Prodi problem for elliptic systems with Trudinger–Moser nonlinearities

Abstract

AbstractIn this work we study the following class of elliptic systems:where Ω ⊂ ℝ2 is a smooth bounded domain, H is a C1 function in [0, +∞)×[0, +∞) which is assumed to be in the critical growth range of Trudinger–Moser type and f1, f2 ∈ Lr (Ω), r > 2. Under suitable hypotheses on the functions a, b, c ∈ C($(\bar\sOm)$ and using variational methods, we prove the existence of two solutions depending on f1 and f2.