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Critical point theorems for nonlinear dynamical systems and their applications. (English) Zbl 1213.49023
Summary: We present some new critical point theorems for nonlinear dynamical systems which are generalizations of Dancš-Hegedüs-Medvegyev’s principle in uniform spaces and metric spaces by applying an abstract maximal element principle established by Lin and Du. We establish some generalizations of Ekeland’s variational principle, Caristi’s common fixed point theorem for multivalued maps, Takahashi’s nonconvex minimization theorem, and the common fuzzy fixed point theorem for τ-functions. Some applications to the existence theorems of nonconvex versions of variational inclusion and disclusion problems in metric spaces are also given.
MSC:
49J52Nonsmooth analysis (other weak concepts of optimality)
49J53Set-valued and variational analysis
37N35Dynamical systems in control
47N10Applications of operator theory in optimization, convex analysis, programming, economics
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