Startseite On a fourth-order Leray–Lions problem involving s(x)-Hardy potential and singular nonlocal source term
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On a fourth-order Leray–Lions problem involving s(x)-Hardy potential and singular nonlocal source term

  • Mohamed Karim Hamdani ORCID logo , Khaled Kefi ORCID logo EMAIL logo , Romulo Diaz Carlos und Zeineb Klai
Veröffentlicht/Copyright: 9. Juli 2025
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Abstract

This paper investigates the existence of at least two distinct weak solutions using Bonanno’s theorem [G. Bonanno, Relations between the mountain pass theorem and local minima, Adv. Nonlinear Anal. 1 (2012), no. 3, 205–220, Theorem 3.2], and establishes the existence of no fewer than two nontrivial weak solutions through the Bonanno–D’Aguì theorem [G. Bonanno and G. D’Aguì, Two nonzero solutions for elliptic Dirichlet problems, Z. Anal. Anwend. 35 (2016), no. 4, 449–464, Theorem 2.1] applied to a general class of fourth-order Leray–Lions problems that include an s ( x ) -Hardy potential and a nonlocal singular term.

Funding statement: The authors thank the Deanship of Scientific Research at Northern Border University, Arar, KSA for funding this research work through the project number NBU-FFR-2025-1706-04. Mohamed Karim Hamdani was supported by the Tunisian Military Research Center for Science and Technology Laboratory LR19DN01.

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Received: 2025-02-03
Revised: 2025-03-03
Accepted: 2025-04-01
Published Online: 2025-07-09

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