A new method for the solvability of mixed hemivariational inequalities

This paper studies the solvability of mixed hemivariational inequalities. A new method for analyzing solvability is proposed, which is based on the projection iteration technique to construct two sequences. At each iteration step, solving hemivariational inequalities is necessary. We then show that the sequences converges strongly to the solution of mixed hemivariational inequalities. This allows the use of the solvability of hemivariational inequalities to guarantee the solvability of mixed hemivariational inequalities. Finally, the applicability of the results is illustrated by the Stokes model of a generalized Newtonian incompressible fluid with nonsmooth nonconvex slip boundary conditions.