Admissible solutions to Hessian equations with exponential growth

• José Francisco de Oliveira ^[1] ; Pedro Ubilla ^[2]
  1. [1] Universidade Federal do Piauí

     Universidade Federal do Piauí

     Brasil

     
  2. [2] Universidad de Santiago de Chile

     Universidad de Santiago de Chile

     Santiago, Chile

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 37, Nº 2, 2021, págs. 749-773
• Idioma: inglés
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• Resumen

  • 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.