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A nodal domain property for the p-Laplacian

Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2000
Summary: We show a partial version of the Courant nodal domain theorem for the \(p\)-Laplacian: any eigenfunction associated to the second eigenvalue has exactly two nodal domains. A similar result is also proved for the Fučik spectrum.
Gossez, Jean-Pierre, Cuesta, M., De Figueiredo, D.   +2 more
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Mixed eigenvalues of p-Laplacian

Frontiers of Mathematics in China, 2015
The mixed principal eigenvalue of p -Laplacian (equivalently, the optimal constant of weighted Hardy inequality in Lp space) is studied in this paper. Several variational formulas for the eigenvalue are presented. As applications of the formulas, a criterion for the positivity of the eigenvalue is obtained.
Ling-Di Wang, Ling-Di Wang, Yuhui Zhang, Mu-Fa Chen   +3 more
openaire   +2 more sources