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Existence and uniqueness for the p(x)-Laplacian-Dirichlet problems

✍ Scribed by Xianling Fan

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
140 KB
Volume
284
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

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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