On the spectrum of the $p$-biharmonic operator involving $p$-Hardy's inequality
Volume 41 / 2014
Applicationes Mathematicae 41 (2014), 239-246
MSC: Primary 35J35; Secondary 35J40.
DOI: 10.4064/am41-2-11
Abstract
In this paper, we study the spectrum for the following eigenvalue problem with the $p$-biharmonic operator involving the Hardy term: $$\varDelta (|\varDelta u|^{p-2}\varDelta u)= \lambda \frac {|u|^{p-2}u}{\delta (x)^{2p}} \hbox { in } \varOmega , \ u\in W_0^{2,p}(\varOmega ).$$ 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.
