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.
@article{25229,
title = {Existence and non-existence of positive solution for (p, q)-Laplacian with singular weights},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {34},
year = {2015},
doi = {10.5269/bspm.v34i2.25229},
language = {EN},
url = {http://dml.mathdoc.fr/item/25229}
}
Zerouali, Abdellah Ahmed; Karim, Belhadj. Existence and non-existence of positive solution for (p, q)-Laplacian with singular weights. Boletim da Sociedade Paranaense de Matemática, Tome 34 (2015) . doi : 10.5269/bspm.v34i2.25229. http://gdmltest.u-ga.fr/item/25229/