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 Existence and multiplicity of solutions for p(x)-Laplacian differential inclusions involving critical growth Ziqing Yuan,Mugen Huang Keywords:Locally Lipschitz, nonsmooth analysis, hemivariational inequality. Abstract: This paper concernes with the existence and multiplicity of solutions for $p(x)$-Laplacian differential inclusions involving critical growth. The main tools are the nonsmooth analysis and variational methods. Our main results generalize some recent results in the literature into nonsmooth cases.