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Local solutions for a nonlinear unilateral problem. (English) Zbl 0613.35051
It is proved existence and uniqueness of local solutions for a unilateral problem for the operators $u\mapsto \partial^ 2u/\partial t^ 2+M(\int_{\Omega}| \nabla u(x,t)|^ 2 dx)(-\Delta u)$ $u\to \partial^ 2u/\partial t^ 2+M(\int_{\Omega}| \nabla u(x,t)|^ 2 dx+\int_{\Omega}u^ 2(x,t)dx)(-\Delta u+u),$ where the real function $$\lambda\mapsto M(\lambda)$$ defined for all $$\lambda\geq 0$$ is continuously differentiable and $$M(\lambda)\geq m_ 0>0$$ for all $$\lambda\geq 0$$.
Reviewer: V.Kostova

MSC:
 35L85 Unilateral problems for linear hyperbolic equations and variational inequalities with linear hyperbolic operators 35A07 Local existence and uniqueness theorems (PDE) (MSC2000)