Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 83, pp. 1-23.

Title: Multiple solutions for p(x)-Kirchhoff type problems with extended Robin boundary conditions

Authors: Houssam Baladi (Univ. of Mohamed Premier, Oujda, Morocco)
         Abdellatif Aglzim (Univ. of Mohamed Premier, Oujda, Morocco)
         Mohammed Filali (Univ. of Mohamed Premier, Oujda, Morocco)
         Najib Tsouli (Univ. of Mohamed Premier, Oujda, Morocco)
  
Abstract:
This article considers p(x)-Kirchhoff type problems with extended 
Robin boundary conditions. Using the mountain pass theorem, Ekeland's 
variational principle, and Krasnoselskii's genus theory, we prove 
the existence at least two, and infinitely many non-trivial weak 
solutions under some suitable conditions on the non-linearities. 
The main results improve and generalize the results introduced in [1].

Submitted July 23, 2024. Published December 11, 2024.
Math Subject Classifications: 35F20, 35F25, 35F30.
Key Words: p(x)-laplacian operator; variational method; Kirchhoff problem;  
    Krasnoselskii's genus; Robin boundary condition.