Resumen de Admissible solutions to Hessian equations with exponential growth

José Francisco de Oliveira, Pedro Ubilla

• 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}u=0in on B,∂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.