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(S)+ property of quasilinear elliptic operators and equations of p(x)-Laplacian type
Fan Xianling * #,Guan Chunxia
Department of Mathematics, Lanzhou University
*Correspondence author
#Submitted by
Subject:
Funding: 国家自然科学基金 (No.10671084)
Opened online:20 February 2008
Accepted by: none
Citation: Fan Xianling ,Guan Chunxia .(S)+ property of quasilinear elliptic operators and equations of p(x)-Laplacian type[OL]. [20 February 2008] http://en.paper.edu.cn/en_releasepaper/content/18732
 
 
Applying the theory of the vector valued Musielak-Orlicz spaces, we give a sufficient condition in order that a quasilinear elliptic operator with the variational structure is of type (S)+, which is stated by the term of the uniform convexity of the corresponding Musielak-Orlicz function. As an application of this result, we obtain the (S)+ property of the operators of the p(x)-Laplacian type and some results on the existence and multiplicity for the equations of the p(x)-Laplacian type, where the operators of the p(x)-Laplacian type are a generalization of the p(x)-Laplacian operator.
Keywords:Musielak-Orlicz space; uniform convexity; mapping of type (S)+; quasilinear elliptic operator; equation of p(x)-Laplacian type
 
 
 

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