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
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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