Carl, S.; Le, Vy K.; Motreanu, D. The sub-supersolution method and extremal solutions for quasilinear hemivariational inequalities. (English) Zbl 1164.35301 Differ. Integral Equ. 17, No. 1-2, 165-178 (2004). 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. Cited in 14 Documents 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 Keywords:sub-supersolution method × Cite Format Result Cite Review PDF