Zerouali, A. and Karim, B.
(2016)
*Existence and non-existence of a positive solution for (p, q)-Laplacian with singular weights.*
Boletim da Sociedade Paranaense de Matematica, 34 (2).
pp. 147-167.

## Abstract

We use the Hardy-Sobolev inequality to study existence and nonexistence results for a positive solution of the quasilinear elliptic problem -Δpu - μΔqu = λmp(x)|u|p-2u + μmq(x)|u|q-2u in Ω 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 < ∞ the results are completely different from those for the usual eigenvalue problem for the 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. © Soc. Paran. de Mat.

Item Type: | Article |
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Subjects: | Mathematics |

Divisions: | SCIENTIFIC PRODUCTION > Mathematics |

Depositing User: | Administrateur Eprints Administrateur Eprints |

Last Modified: | 31 Jan 2020 15:48 |

URI: | http://eprints.umi.ac.ma/id/eprint/4007 |

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