Steklov problem with an indefinite weight for the p-Laplacian
| dc.contributor.author | Torne, Olaf | |
| dc.date.accessioned | 2021-06-01T13:50:12Z | |
| dc.date.available | 2021-06-01T13:50:12Z | |
| dc.date.issued | 2005-08-14 | |
| dc.description.abstract | Let 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.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 8 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Torné, O. (2005). Steklov problem with an indefinite weight for the p-Laplacian. <i>Electronic Journal of Differential Equations, 2005</i>(87), pp. 1-9. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13688 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Nonlinear eigenvalue problem | |
| dc.subject | Steklov problem | |
| dc.subject | p-Laplacian | |
| dc.subject | Nonlinear boundary conditions | |
| dc.subject | Indefinite weight | |
| dc.title | Steklov problem with an indefinite weight for the p-Laplacian | |
| dc.type | Article |