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

Abstract

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.

Keywords

• parabolic variation-inequality problems
• weak solution
• variable parameter kirchhoff operators not in divergence form
• existence
• uniqueness
• stability
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