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    Author(s)

    Eugenio Cabanillas Lapa, PhD. Willy Barahona Martinez — Academia (Universities, Colleges and other higher learning entities) (Instituto de Investigaci´on, Facultad de Ciencias Matem´aticas-UNMSM, Lima, Per´u), PhD. Benigno Godoy Torres — Academia (Universities, Colleges and other higher learning entities) (Instituto de Investigaci´on, Facultad de Ciencias Matem´aticas-UNMSM, Lima, Per´u), PhD. Gabriel Rodriguez Varillas — Academia (Universities, Colleges and other higher learning entities) (Instituto de Investigaci´on, Facultad de Ciencias Matem´aticas-UNMSM, Lima, Per´u)
    Category: Mathematics
    DOI: https://armjmath.sci.am/index.php/ajm/article/view/103
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      Existence of Solutions for SemilinearIntegro-differential Equations of p-Kirchhoff Type

      Eugenio Cabanillas Lapa, PhD. Willy Barahona Martinez — Academia (Universities, Colleges and other higher learning entities) (Instituto de Investigaci´on, Facultad de Ciencias Matem´aticas-UNMSM, Lima, Per´u), PhD. Benigno Godoy Torres — Academia (Universities, Colleges and other higher learning entities) (Instituto de Investigaci´on, Facultad de Ciencias Matem´aticas-UNMSM, Lima, Per´u), PhD. Gabriel Rodriguez Varillas — Academia (Universities, Colleges and other higher learning entities) (Instituto de Investigaci´on, Facultad de Ciencias Matem´aticas-UNMSM, Lima, Per´u)
      This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

      Submitted: 2024-12-18; Published: 2015-01-31
      © 2025 by author(s) and The Gufo Inc.
      CC BY-NC 4.0 This work is licensed under Creative Commons Attribution–NonCommercial International License (CC BY-NC 4.0).

      Abstract

      In our research we will study the existence of weak solutions to the problem−[M(‖u‖p1,p)]p−1∆pu=f(x,u) +∫Ωk(x,y)H(u)dyin Ω,with zero Dirichlet boundary condition on a bounded smooth domain ofRn,1< p < N;M,f,kandHare given functions. By means of the Galerkin methodand using of the Brouwer Fixed Point theorem we get our results. The uniquenessof a weak solution is also considered.

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