Geodesic
Unilateral problems for the Klein-Gordon operator with nonlinearity of Kirchhoff-Carrier type
Electronic journal of differential equations, Tome 2015 (2015)
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},
     year = {2015},
     volume = {2015},
     zbl = {1329.35216},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a64/}
}
TY  - JOUR
AU  - Raposo,  Carlos
AU  - Pereira,  Ducival
AU  - Araujo,  Geraldo
AU  - Baena,  Antonio
TI  - Unilateral problems for the Klein-Gordon operator with nonlinearity of Kirchhoff-Carrier type
JO  - Electronic journal of differential equations
PY  - 2015
VL  - 2015
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LA  - en
ID  - EJDE_2015__2015__a64
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%A Baena,  Antonio
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%J Electronic journal of differential equations
%D 2015
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%U http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a64/
%G en
%F EJDE_2015__2015__a64
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/