Evolutionary variational–hemivariational inequalities: Existence and comparison results

We consider an evolutionary quasilinear hemivariational inequality under constraints represented by some closed and convex subset. Our main goal is to systematically develop the method of sub-supersolution on the basis of which we then prove existence, comparison, compactness and extremality results. The obtained results are applied to a general obstacle problem. We improve the corresponding results in the recent monograph [S. Carl, V.K. Le, D. Motreanu, Nonsmooth Variational Problems and Their Inequalities. Comparison Principles and Applications, Springer Monogr. Math., Springer, New York, 2007].