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Sub-super-solution method for a class of higher order evolution hemivariational inequalities. (English) Zbl 1162.49015

Summary: 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 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.

MSC:

49J40 Variational inequalities
35K90 Abstract parabolic equations
47J35 Nonlinear evolution equations
47J20 Variational and other types of inequalities involving nonlinear operators (general)
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