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February 21, 2026

Multiplicity results for sixth-order nonlinear elliptic equations involving the p ( x )-triharmonic operator with Navier conditions

Key Points

The research aims to explore multiplicity results for sixth-order nonlinear elliptic equations involving the p(x)-triharmonic operator under Navier boundary conditions.
Analysis of the sixth-order nonlinear elliptic equation framework
Application of variational techniques for multiplicity
Examination of boundary conditions to derive solution existence
Identified multiple solution branches for the nonlinear elliptic equations
Showed the influence of Navier conditions on solution behavior
Established criteria under which multiple solutions exist

Abstract

Abstract We study the following nonlinear problem: - Δ p ⁢ (x) 3 ⁢ u + | u | p ⁢ (x) - 2 ⁢ u = λ ⁢ a ⁢ (x) ⁢ f ⁢ (x, u) + μ ⁢ g ⁢ (x, u) in ⁢ Ω, u = Δ ⁢ u = Δ 2 ⁢ u = 0 on ⁢ ∂ ⁡ Ω, \{aligned {-^3₏ (ₗ) u+|u|^p (x) -2u&% = a (x) f (x, u) + g (x, u) && %, \\ u= u=^2u&=0&&% on, aligned. where Ω ⊂ ℝ N ^{N}</jats: tex

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