On an open problem involving the p ( x ) -Laplacian—A further study on the multiplicity of weak solutions to p ( x ) -Laplacian equations

On an open problem involving the p ( x ) -Laplacian—A further study on the multiplicity of weak solutions to p ( x ) -Laplacian equations

By using a variational method and the truncation technique, we show the multiplicity of weak solutions to a class of p ( x ) -Laplacian equations. An open problem proposed by Professor Xianling Fan is solved and more general results are given in this paper.

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Veröffentlicht in:Nonlinear analysis 2008-08, Vol.69 (4), p.1445-1453
Hauptverfasser: Yao, Jinghua, Wang, Xiaoyan
Format: Artikel
Sprache:eng
Schlagworte:
[formula omitted]-Laplacian
Algebra
Commutative rings and algebras
Critical point
Exact sciences and technology
Functional analysis
Mathematical analysis
Mathematics
Partial differential equations
Sciences and techniques of general use
Symmetric mountain pass lemma
Variable exponent Sobolev space
Weak solution
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Zusammenfassung:By using a variational method and the truncation technique, we show the multiplicity of weak solutions to a class of p ( x ) -Laplacian equations. An open problem proposed by Professor Xianling Fan is solved and more general results are given in this paper.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2007.06.044