Unilateral problems for the Klein-Gordon operator with nonlinearity of Kirchhoff-Carrier type
Carlos Alberto Raposo, Ducival Carvalho Pereira, Geraldo Araújo, Antonio Baena · DOAJ (DOAJ: Directory of Open Access Journals) · 2015
This work concerns the unilateral problem for the Klein-Gordon operator $$ \mathbb{L}=\frac{\partial^2 u}{\partial t^2}-M(| abla u|^2)\Delta u+M_1(|u|^2)u-f. $$ Using an appropriate penalization, we obtain a variational inequality for a perturbed equation, and then show the existence and uniqueness of solutions.