Admissible Solutions to Hessian Equations with Exponential Growth

The aim of this paper is to prove the existence of radially symmetric k-Admissible solutions for the following Dirichlet problem associated with the k-Th Hessian operator: Sk[u] = f(x,-u) u < 0-in B, u = 0 on B, where B is the unit ball of RN, N = 2k (k € N), and f : B × R → R behaves like exp(u(N+2)/N) when u → ∞ and satisfies the Ambrosetti Rabinowitz condition. Our results constitute the exponential counterpart of the existence theorems of Tso (1990) for power-Type nonlinearities under the condition N >2k. © 2021 European Mathematical Society Publishing House. All rights reserved.