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The Dirichlet problem for the vector ordinary\(p\)-Laplacian

✍ Scribed by Song, Yawei; Thompson, Bevan

Book ID
125379105
Publisher
Springer-Verlag
Year
2014
Tongue
English
Weight
297 KB
Volume
47
Category
Article
ISSN
1598-5865

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## Abstract Two results on the existence and uniqueness for the __p__(__x__)‐Laplacian‐Dirichlet problem βˆ’__div__(|βˆ‡__u__|^__p__(__x__) βˆ’ 2^βˆ‡__u__) = __f__(__x__, __u__) in Ξ©, __u__ = 0 on βˆ‚Ξ©, are obtained. The first one deals with the case that __f__(__x__, __u__) is nonincreasing in __u__. The se

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This paper presents several su cient conditions for the existence of solutions for the Dirichlet problem of p(x)-Laplacian Especially, an existence criterion for inΓΏnite many pairs of solutions for the problem is obtained. The discussion is based on the theory of the spaces L p(x) ( ) and W 1;p(x)