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Multiplicity results for a fourth-order elliptic equation of p(x)-kirchhoff type with weights

  • Khaled Kefi EMAIL logo , Nguyen Thanh Chung and Zohreh Naghizadeh
Published/Copyright: August 9, 2025
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Abstract

This paper deals with a class of fourth-order elliptic equations of p(x)-Kirchhoff type of the form

Δp(x)2uMΩ1p(x)|u|p(x)dxΔp(x)u=λW(x)|u|q(x)2u in Ω,u=Δu=0 on Ω,

where Ω N (N ≥ 2) is a smooth bounded domain with boundary Ω,p:ΩR is a log-Hölder continuous function, M(t) = a + btκ is a Kirchhoff function with a,κ>0,b0,Δp(x)2u= Δ(|Δu|p(x)2Δu) is the operator of fourth order called the p(x)-biharmonic operator, Δp(x)u = div (|∇u|p(x)2∇u) is the p(x)-Laplacian, W : Ω ℝ is a weighted function and λ is a positive parameter. Using variational techniques, we establish some multiplicity results to the problem in two cases when the function W is sign-changing or not and two examples are given to illustrate the main results.


The authors extend their appreciation to the Deanship of Scientific Research at Northern Border University, Arar, KSA for funding this research work through the project number NBU-FFR-2024-1706-06.


  1. (Communicated by Alberto Lastra)

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Received: 2024-09-25
Accepted: 2025-05-23
Published Online: 2025-08-09
Published in Print: 2025-08-26

© 2025 Mathematical Institute Slovak Academy of Sciences

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