In the study of a wide range of nonlinear elliptic and parabolic boundary value problems, the method of sub-supersolution has been proved to play an eminent role. This method is a powerful tool for establishing existence and enclosure results when coercivity of the operators related to the abstract formulation of the problems under consideration fails. Further qualitative properties such as the multiplicity and location of solutions or the existence of extremal solutions can also be investigated by means of the sub-supersolution method. As stationary and evolutionary variational inequalities of nonpotential type include, in general, nonlinear elliptic and parabolic boundary value problems as particular cases, it is desirable to extend the sub-supersolution method to variational inequalities in a way that preserves its characteristic features.
S. Carl and V. K. Le, "Introduction," Springer Monographs in Mathematics, pp. 1-8, Springer, Mar 2021.
The definitive version is available at https://doi.org/10.1007/978-3-030-65165-7_1
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03 Mar 2021