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A critical point theory for nonsmooth functionals. (English) Zbl 0828.58006
In this paper a suitable definition of “norm of differential” and the notion of critical points are introduced for continuous functionals on metric spaces. By means of this new definition, the classical results of Lyusternik-Schnirelmann on critical point theory for smooth functionals on manifolds are extended to continuous functionals on complete metric spaces. Applications of these new techniques are presented to obtain a multiplicity result on solutions of an elliptic variational inequality.

MSC:
58E05Abstract critical point theory
58E35Variational inequalities (global problems)
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