• Nonlinear Functional Analysis and Applications
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• 제27권2호
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• pp.349-361
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• 2022

In this paper, we study the following nonlinear problem: $$\{-\Delta_{p}^{3}(x)u\;=\;{\lambda}V_{1}(x){\mid}u{\mid}^{q(x)-2}u\;in\;{\Omega},\\u\;=\;{\Delta}u\;{\Delta}^{2}u\;=\;0\;on\;{\partial}\Omega, $$ under adequate conditions on the exponent functions p, q and the weight function V₁. We prove the existence and nonexistence of eigenvalues for p(x)-triharmonic problem with Navier boundary value conditions on a bounded domain in ℝ^N. Our technique is based on variational approaches and the theory of variable exponent Lebesgue spaces.