Geodesic
Existence and multiplicity of solutions to operator equations involving duality mappings on Sobolev spaces with variable exponents
Electronic Journal of Differential Equations, Tome 2015 (2015).

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Summary: The aim of this article is to study the existence and multiplicity of solutions of operator equations involving duality mappings on Sobolev spaces with variable exponents. Our main tools are the well known Mountain Pass Theorem and its $\mathbb{Z} _2$-symmetric version.
Classification : 35J60, 35B38, 47J30, 46E30
Keywords: mountain pass theorem, duality mapping, critical point, Sobolev space with variable exponent 
@article{EJDE_2015__2015__a66,
     author = {Matei, Pavel},
     title = {Existence and multiplicity of solutions to operator equations involving duality mappings on {Sobolev} spaces with variable exponents},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2015},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a66/}
}
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Matei, Pavel. Existence and multiplicity of solutions to operator equations involving duality mappings on Sobolev spaces with variable exponents. Electronic Journal of Differential Equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a66/