Some results for a p(x)-Kirchhoff type variation-inequality problems in non-divergence form

The author of this article concerns with the existence, uniqueness, and stability of the weak solution to the variation-inequality problem. The Kirchhoff operator is a non-divergence form with space variable parameter. The existence of generalized solution is proved by the Leray-Schauder principle and parabolic regularization. The uniqueness and stability of the solution are also discussed by contradiction.