Geodesic
On a~nonlinear eigenvalue problem in Sobolev spaces with variable exponent
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 208-217

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We consider a class of nonlinear Dirichlet problems involving the $p(x)$–Laplace operator. Our framework is based on the theory of Sobolev spaces with variable exponent and we establish the existence of a weak solution in such a space. The proof relies on the Mountain Pass Theorem. 
@article{SEMR_2005_2_a12,
     author = {T.-L. Dinu},
     title = {On a~nonlinear eigenvalue problem in {Sobolev} spaces with variable exponent},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {208--217},
     publisher = {mathdoc},
     volume = {2},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2005_2_a12/}
}
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T.-L. Dinu. On a~nonlinear eigenvalue problem in Sobolev spaces with variable exponent. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 208-217. http://geodesic.mathdoc.fr/item/SEMR_2005_2_a12/