Hamiltonian elliptic systems with critical polynomial-exponential growth. (January 2022) - do Ó, João Marcos; Macedo, Abiel; Ribeiro, Bruno
Abstract: In this work, we revisit a classical problem of Hamiltonian-type systems of second-order elliptic PDE in bounded domains. Recalling the famous critical hyperbola associated with this problem, we propose an approach where one of the nonlinearities has a polynomial growth over this hyperbola's asymptotes, which allows the other one to have exponential growth. We establish solutions for these critical systems by using the reduction by inversion method and some new results for sharp Adams Inequality and Concentration–Compactness for high order N -Laplace operators.