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

Abdelouahed El Khalil, My Driss Morchid Alaoui, and Abdelfattah Touzani. "On the spectrum of the p-biharmonic operator involving p-Hardy's inequality." Applicationes Mathematicae 41.2-3 (2014): 239-246. <http://eudml.org/doc/280054>.

@article{AbdelouahedElKhalil2014,
abstract = {In this paper, we study the spectrum for the following eigenvalue problem with the p-biharmonic operator involving the Hardy term: $Δ(|Δu|^\{p-2\} Δu) = λ(|u|^\{p-2\}u)/(δ(x)^\{2p\})$ in Ω, $u ∈ W₀^\{2,p\}(Ω)$. 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.},
author = {Abdelouahed El Khalil, My Driss Morchid Alaoui, Abdelfattah Touzani},
journal = {Applicationes Mathematicae},
keywords = {-biharmonic operator; eigenvalues; duality mapping; variational technique; Palais-Smale condition; Hardy-Rellich inequality},
language = {eng},
number = {2-3},
pages = {239-246},
title = {On the spectrum of the p-biharmonic operator involving p-Hardy's inequality},
url = {http://eudml.org/doc/280054},
volume = {41},
year = {2014},
}

TY - JOUR
AU - Abdelouahed El Khalil
AU - My Driss Morchid Alaoui
AU - Abdelfattah Touzani
TI - On the spectrum of the p-biharmonic operator involving p-Hardy's inequality
JO - Applicationes Mathematicae
PY - 2014
VL - 41
IS - 2-3
SP - 239
EP - 246
AB - In this paper, we study the spectrum for the following eigenvalue problem with the p-biharmonic operator involving the Hardy term: $Δ(|Δu|^{p-2} Δu) = λ(|u|^{p-2}u)/(δ(x)^{2p})$ in Ω, $u ∈ W₀^{2,p}(Ω)$. 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.
LA - eng
KW - -biharmonic operator; eigenvalues; duality mapping; variational technique; Palais-Smale condition; Hardy-Rellich inequality
UR - http://eudml.org/doc/280054
ER -