Geodesic
Existence and multiplicity of solutions for a differential inclusion problem involving the \(p(x)\)-Laplacian
Electronic journal of differential equations, Tome 2010 (2010)
In this article we consider the differential inclusion

$\displaylines{ -\hbox{div}(|\nabla u|^{p(x)-2}\nabla u)\in \partial F(x,u) \quad\hbox{in }\Omega,\cr u=0 \quad \hbox{on }\partial \Omega }$

which involves the $p(x)$-Laplacian. By applying the nonsmooth Mountain Pass Theorem, we obtain at least one nontrivial solution; and by applying the symmetric Mountain Pass Theorem, we obtain k-pairs of nontrivial solutions in $W_{0}^{1,p(x)}(\Omega)$.
Classification : 35J20, 35J70, 35R70
Keywords: $p(x)$-Laplacian, nonsmooth mountain pass theorem, differential inclusion 
@article{EJDE_2010__2010__a261,
     author = {Dai,  Guowei},
     title = {Existence and multiplicity of solutions for a differential inclusion problem involving the {\(p(x)\)-Laplacian}},
     journal = {Electronic journal of differential equations},
     year = {2010},
     volume = {2010},
     zbl = {1190.35231},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a261/}
}
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%A Dai,  Guowei
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%J Electronic journal of differential equations
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%F EJDE_2010__2010__a261
Dai,  Guowei. Existence and multiplicity of solutions for a differential inclusion problem involving the \(p(x)\)-Laplacian. Electronic journal of differential equations, Tome 2010 (2010). http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a261/