Existence and non-existence of positive solution for (p, q)-Laplacian with singular weights
| Autor: | Abdellah Ahmed Zerouali, Belhadj Karim |
|---|---|
| Jazyk: | English<br />Portuguese |
| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Boletim da Sociedade Paranaense de Matemática, Vol 34, Iss 2, Pp 147-167 (2016) |
| Druh dokumentu: | article |
| ISSN: | 0037-8712 2175-1188 |
| DOI: | 10.5269/bspm.v34i2.25229 |
| Popis: | We use the Hardy-Sobolev inequality to study existence and non-existence results for a positive solution of the quasilinear elliptic problem -\Delta{p}u − \mu \Delta{q}u = \limda[mp(x)|u|p−2u + \mu mq(x)|u|q−2u] in \Omega driven by nonhomogeneous operator (p, q)-Laplacian with singular weights under the Dirichlet boundary condition. We also prove that in the case where μ > 0 and with 1 < q < p < \infinity the results are completely different from those for the usual eigenvalue for the problem p-Laplacian with singular weight under the Dirichlet boundary condition, which is retrieved when μ = 0. Precisely, we show that when μ > 0 there exists an interval of eigenvalues for our eigenvalue problem. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|