Abstract
Differential-operator inclusions and multivariational inequalities in Banach spaces with quasimonotone mappings are considered. The functional-topological properties of resolving operators are investigated. The Faedo---Galerkin method for noncoercive mappings and the finite-difference and Dubinsky methods for differential-operator inclusions in Banach spaces with pseudomonotone mappings are substantiated. Important a priori estimates are obtained.
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