Infinitely many solutions for a differential inclusion problem in involving p(x)-Laplacian and oscillatory terms

In this paper, we consider the differential inclusion in involving the p ( x )-Laplacian of the type where is Lipschitz continuous function satisfying some given assumptions. The approach used in this paper is the variational method for locally Lipschitz functions. Under suitable oscillatory assumpt...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2012, Vol.63 (4), p.691-711
Main Authors: Ge, Bin, Zhou, Qing-Mei, Xue, Xiao-Ping
Format: Article
Language:English
Subjects:
Engineering
Mathematical Methods in Physics
Theoretical and Applied Mechanics
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Summary:In this paper, we consider the differential inclusion in involving the p ( x )-Laplacian of the type where is Lipschitz continuous function satisfying some given assumptions. The approach used in this paper is the variational method for locally Lipschitz functions. Under suitable oscillatory assumptions on the potential F at zero or at infinity, we show the existence of infinitely many solutions of (P). We also establish a Bartsch-Wang type compact embedding theorem for variable exponent spaces.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-012-0192-1