Local solutions for a nonlinear unilateral problem. (English) Zbl 0613.35051

Medeiros, L. A.; Milla Miranda, M.

Rev. Roum. Math. Pures Appl. 31, 371-382 (1986).

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)

Keywords:

existence; uniqueness; local solutions; unilateral problem