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The sub-supersolution method and extremal solutions for quasilinear hemivariational inequalities. (English) Zbl 1164.35301

Summary: We generalize the sub-supersolution method known for weak solutions of single and multivalued equations to quasilinear elliptic hemivariational inequalities. We first introduce the fundamental notion of sub- and supersolutions and prove on this basis existence, comparison, compactness, and extremality results for the hemivariational inequalities under consideration.

MSC:

35A15 Variational methods applied to PDEs
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35J20 Variational methods for second-order elliptic equations
49J52 Nonsmooth analysis
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