Existence and non-existence of positive solution for (p, q)-Laplacian with singular weights
2015 ◽
Vol 34
(2)
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pp. 147-167
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Keyword(s):
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.
2012 ◽
Vol 11
(5)
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pp. 1825-1838
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2020 ◽
Vol 11
(1)
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pp. 1
2014 ◽
Vol 16
(04)
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pp. 1350048
2007 ◽
Vol 12
(2)
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pp. 143-155
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2010 ◽
Vol 140
(2)
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pp. 435-447
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2017 ◽
Vol 63
(9)
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pp. 1322-1340
Keyword(s):