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.

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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
Subjects: Mathematics
Divisions: SCIENTIFIC PRODUCTION > Mathematics
Depositing User: Administrateur Eprints Administrateur Eprints
Last Modified: 31 Jan 2020 15:48

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