Geodesic
Existence and multiplicity of solutions for a differential inclusion problem involving the $p(x)$-Laplacian
Electronic Journal of Differential Equations, Tome 2010 (2010).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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__a61,
     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},
     publisher = {mathdoc},
     volume = {2010},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a61/}
}
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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__a61/