Existence results for a class of local and nonlocal nonlinear elliptic problems

• Autores: Said Ait Temghart, Chakir Allalou, Adil Abbassi
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 25, Nº. 1, 2023, págs. 1-21
• Idioma: inglés
• DOI: 10.56754/0719-0646.2501.001
• Enlaces
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• Resumen
  • español

    En este artículo, estudiamos los problemas p-Laplacianos en el caso donde p depende de la solución misma. Consideramos dos situaciones, cuando p es una cantidad local y no-local. Usando una técnica de perturbación singular, demostramos la existencia de soluciones débiles para el problema asociado a la siguiente ecuación y también para su versión no-local. El principal objetivo de este artículo es extender los resultados establecidos por M. Chipot y H. B. de Oliveira (Math. Ann., 2019, 375, 283-306).

  • English

    In this paper, we study the p-Laplacian problems in the case where p depends on the solution itself. We consider two situations, when p is a local and nonlocal quantity. By using a singular perturbation technique, we prove the existence of weak solutions for the problem associated to the following equation and also for its nonlocal version. The main goal of this paper is to extend the results established by M. Chipot and H. B. de Oliveira (Math. Ann., 2019, 375, 283-306).

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