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dc.contributor.authorTorne, Olaf ( )
dc.date.accessioned2021-06-01T13:50:12Z
dc.date.available2021-06-01T13:50:12Z
dc.date.issued2005-08-14
dc.identifier.citationTorné, O. (2005). Steklov problem with an indefinite weight for the p-Laplacian. Electronic Journal of Differential Equations, 2005(87), pp. 1-9.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/13688
dc.description.abstractLet Ω ⊂ ℝN, with N ≥ 2, be a Lipschitz domain and let 1 < p < ∞. We consider the eigenvalue problem ∆2u = 0 in Ω and |∇u|p-2 ∂u/∂v = λm|u|p-2u on ∂Ω, where λ is the eigenvalue and u ∈ W1,p(Ω) is an associated eigenfunction. The weight m is assumed to lie in an appropriate Lebesgue space and may change sign. We sketch how a sequence of eigenvalues may be obtained using infinite dimensional Ljusternik-Schnirelman theory and we investigate some of the nodal properties of eigenfunctions associated to the first and second eigenvalues. Amongst other results we find that if m+ ≢ 0 and ∫∂Ωmdσ < 0 then the first positive eigenvalue is the only eigenvalue associated to an eigenfunction of definite sign and any eigenfunction associated to the second positive eigenvalue has exactly two nodal domains.
dc.formatText
dc.format.extent8 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University-San Marcos, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectNonlinear eigenvalue problemen_US
dc.subjectSteklov problemen_US
dc.subjectp-Laplacianen_US
dc.subjectNonlinear boundary conditionsen_US
dc.subjectIndefinite weighten_US
dc.titleSteklov problem with an indefinite weight for the p-Laplacianen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
dc.description.departmentMathematics


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