Electron. J. Differential Equations, Vol. 2024 (2024), No. 83, pp. 1-23.

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

Houssam Baladi, Abdellatif Aglzim, Mohammed Filali, Najib Tsouli

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
DOI: 10.58997/ejde.2024.83

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Houssam Baladi
University of Mohamed Premier
Mathematics Department, Faculty of Science
Oujda, Morocco
email: houssam.baladi@ump.ac.ma
Abdellatif Aglzim
University of Mohamed Premier
Mathematics Department
Faculty of Science, Oujda, Morocco
email: abdellatif.aglzim@ump.ac.ma
Mohammed Filali
University of Mohamed Premier
Mathematics Department
Faculty of Science, Oujda, Morocco
email: filali1959@yahoo.fr
Najib Tsouli
University of Mohamed Premier
Mathematics Department
Faculty of Science
Oujda, Morocco
email: n.tsouli@ump.ac.ma

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