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On the spectrum of the p-biharmonic operator involving p-Hardy's inequality

Abdelouahed El Khalil, My Driss Morchid Alaoui, Abdelfattah Touzani (2014)

Applicationes Mathematicae

In this paper, we study the spectrum for the following eigenvalue problem with the p-biharmonic operator involving the Hardy term: Δ ( | Δ u | p - 2 Δ u ) = λ ( | u | p - 2 u ) / ( δ ( x ) 2 p ) in Ω, u W 2 , p ( Ω ) . 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.

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