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.


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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