Geodesic
Unilateral problems for the Klein-Gordon operator with nonlinearity of Kirchhoff-carrier type
Electronic Journal of Differential Equations, Tome 2015 (2015).

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

Summary: This work concerns the unilateral problem for the Klein-Gordon operator $$ \mathbb{L}=\frac{\partial^2 u}{\partial t^2}-M(|\nabla u|^2)\Delta u+M_1(|u|^2)u-f. $$ Using an appropriate penalization, we obtain a variational inequality for a perturbed equation, and then show the existence and uniqueness of solutions.
Classification : 35K60, 35F30
Keywords: unilateral problem, Kirchhoff-carrier, Klein-Gordon equation, weak solution, uniqueness of solutions 
@article{EJDE_2015__2015__a64,
     author = {Raposo, Carlos and Pereira, Ducival and Araujo, Geraldo and Baena, Antonio},
     title = {Unilateral problems for the {Klein-Gordon} operator with nonlinearity of {Kirchhoff-carrier} type},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2015},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a64/}
}
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Raposo, Carlos; Pereira, Ducival; Araujo, Geraldo; Baena, Antonio. Unilateral problems for the Klein-Gordon operator with nonlinearity of Kirchhoff-carrier type. Electronic Journal of Differential Equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a64/