Sub–super-solution method for a class of higher order evolution hemivariational inequalities ☆

Abstract In this paper, we extend the extremality results for the variational inequality to a higher order evolution hemivariational inequality. More precisely, we give an existence theorem of solution for the higher order evolution hemivariational inequality by using the sub–super-solution method. We prove the compactness of the solution set within an order interval formed by the sub-solution and super-solution. We also show an existence theorem of the extremal solution for the higher order evolution hemivariational inequality under consideration.

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