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Global attractors of nonautonomous disperse dynamical systems and differential inclusions. (English) Zbl 1001.37012
The authors study the longtime behavior of abstract nonautonomous dynamical systems without uniqueness. The main result of the paper is the extention of the attractors theory to the class of dissipative nonautonomous dynamical systems generated by multivalued (set-valued) operators. The applications of the obtained results to ordinary differential equations with non Lipschitz nonlinearities, differential inclusions and functional-differential equations are also considered. The alternative approach to nonautonomous dynamical systems without uniqueness which is based on the concept of a trajectory dynamical system and trajectory attractors can be found in [V. V. Chepyzhov and M. I. Vishik, Attractors for equations of mathematical physics. Colloquium Publications. 49. Providence, RI: American Mathematical Society (2002; Zbl 0986.35001)].

MSC:
37B55 Topological dynamics of nonautonomous systems
34A60 Ordinary differential inclusions
34D45 Attractors of solutions to ordinary differential equations
34K06 Linear functional-differential equations
37B25 Stability of topological dynamical systems
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