The topological degree methods for the fractional p(·)-Laplacian problems with discontinuous nonlinearities

• Autores: Hasnae El Hammar, Chakir Allalou, Adil Abbassi, Abderrazak Kassidi
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 24, Nº. 1, 2022, págs. 63-82
• Idioma: inglés
• DOI: 10.4067/S0719-06462022000100063
• Enlaces
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• Resumen
  • español

    RESUMEN En este artículo, usamos el grado topológico basado en la ecuación abstracta de Hammerstein para investigar la existencia de soluciones débiles para una clase de problemas elípticos de valor en la frontera de Dirichlet que involucran el operador p(x)-Laplaciano fraccional con no linealidades discontinuas. El marco funcional apropiado para estos problemas es el espacio de Sobolev fraccional con exponente variable.

  • English

    ABSTRACT In this article, we use the topological degree based on the abstract Hammerstein equation to investigate the existence of weak solutions for a class of elliptic Dirichlet boundary value problems involving the fractional p(x)-Laplacian operator with discontinuous nonlinearities. The appropriate functional framework for this problems is the fractional Sobolev space with variable exponent.

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