Eigenvalue Problems for the p-Laplacian with Indefinite Weights
| dc.contributor.author | Cuesta, Mabel | |
| dc.date.accessioned | 2020-02-21T15:08:26Z | |
| dc.date.available | 2020-02-21T15:08:26Z | |
| dc.date.issued | 2001-05-10 | |
| dc.description.abstract | We consider the eigenvalue problem -∆pu = λV(x) |u|p-2 u, u ∈ W1,p0 (Ω) where p > 1, ∆p is the p-Laplacian operator, λ > 0, Ω is a bounded domain in ℝN and V is a given function in Ls (Ω) (s depending on p and N). The weight function V may change sign and has nontrivial positive part. We prove that the least positive eigenvalue is simple, isolated in the spectrum and it is the unique eigenvalue associated to a nonnegative eigenfunction. Furthermore, we prove the strict monotonicity of the least positive eigenvalue with respect to the domain and the weight. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 9 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Cuesta, M. (2001). Eigenvalue problems for the p-Laplacian with indefinite weights. <i>Electronic Journal of Differential Equations, 2001</i>(33), pp. 1-9. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/9326 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, 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, 2001, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Nonlinear eigenvalue problem | |
| dc.subject | p-Laplacian | |
| dc.subject | Indefinite weight | |
| dc.title | Eigenvalue Problems for the p-Laplacian with Indefinite Weights | |
| dc.type | Article |