Electron. J. Diff. Equ., Vol. 2015 (2015), No. 137, pp. 1-14.

Unilateral problems for the Klein-Gordon operator with nonlinearity of Kirchhoff-Carrier type

Carlos Raposo, Ducival Pereira, Geraldo Araujo, Antonio Baena

Abstract:
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.

Submitted July 29, 2014. Published May 20, 2015.
Math Subject Classifications: 35K60, 35F30.
Key Words: Unilateral problem; Kirchhoff-Carrier; Klein-Gordon equation; weak solution; uniqueness of solutions.

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Carlos Raposo
Department of Mathematics, Federal University of São João Del-Rei
São João Del-Rei - MG 36307-352, Brazil
email: raposo@ufsj.edu.br
Ducival Pereira
Department of Mathematics, State University of Pará
Belém - PA 66113-200, Brazil
email: ducival@oi.com.br
Geraldo Araujo
Department of Mathematics, Federal University of Pará
Belém - PA 66075-110, Brazil
email: gera@ufpa.br
Antonio Baena
Department of Mathematics, Federal University of Pará
Belém - PA 66075-110, Brazil
email: baena@ufpa.br

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