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Existence and uniqueness for the p ( x )‐Laplacian‐Dirichlet problems
Author(s) -
Fan Xianling
Publication year - 2011
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200810203
Subject(s) - uniqueness , mathematics , dirichlet distribution , combinatorics , dirichlet problem , laplace operator , pure mathematics , mathematical analysis , boundary value problem
Two results on the existence and uniqueness for the p ( x )‐Laplacian‐Dirichlet problem − div (|∇ u | p ( x ) − 2 ∇ u ) = f ( x , u ) in Ω, u = 0 on ∂Ω, are obtained. The first one deals with the case that f ( x , u ) is nonincreasing in u . The second one deals with the radial case in which f ( r , u ) is nondecreasing in u and satisfies the sub‐ p − − 1 growth condition. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim
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