Some results for a variation-inequality problem with fourth order p(x)-Kirchhoff operator arising from options on fresh agricultural products

In this paper, we study variation-inequality initial-boundary value problems with fouth order $ p(x) $-Kirchhoff operators. First, an operator is constructed based on the Leray Schauder principle, and the existence of solutions is obtained. Secondly, the stability and uniqueness of the solution are analyzed after the conditions are appropriately relaxed on the Kirchhoff operators.