A priori bounds and existence of solutions for some nonlocal elliptic problems

• Begoña Barrios ^[1] ; Leandro M. Del Pezzo ^[2] ; Jorge García-Melián ^[3] ; Alexander Quaas ^[4]
  1. [1] University of Texas at Austin

     University of Texas at Austin

     Estados Unidos

     
  2. [2] Universidad de Buenos Aires

     Universidad de Buenos Aires

     Argentina

     
  3. [3] Universidad de La Laguna

     Universidad de La Laguna

     San Cristóbal de La Laguna, España

     
  4. [4] Universidad Técnica Federico Santa María

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 34, Nº 1, 2018, págs. 195-220
• Idioma: inglés
• DOI: 10.4171/RMI/983
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• Resumen

  • In this paper we show existence of solutions for some elliptic problems with nonlocal diffusion by means of nonvariational tools. Our proof is based on the use of topological degree, which requires a priori bounds for the solutions. We obtain the a priori bounds by adapting the classical scaling method of Gidas and Spruck. We also deal with problems involving gradient terms.