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In this paper, we study the spectrum for the following eigenvalue problem with the p-biharmonic operator involving the Hardy term: ${\Delta \left(\right|\Delta u|}^{p-2}{\Delta u)=\lambda (\left|u\right|}^{p-2}u)/\left(\delta {\left(x\right)}^{2p}\right)$ in Ω, $u\in W{₀}^{2,p}\left(\Omega \right)$. By using the variational technique and the Hardy-Rellich inequality, we prove that the above problem has at least one increasing sequence of positive eigenvalues.

We study the existence of solutions for a p-biharmonic problem with a critical Sobolev exponent and Navier boundary conditions, using variational arguments. We establish the existence of a precise interval of parameters for which our problem admits a nontrivial solution.