Topological structure of solution sets of differential inclusions: the constrained case. (English) Zbl 1021.49019

The paper presents important results dealing not only with the existence of solutions, but also studying the topological structure of the solution set of semilinear differential inclusions on closed subsets of Banach spaces. The problem is closely related to the invariance or viability property of a trajectory with respect to a prescribed set. New results are given in the case of regular and strictly regular sets. Applications concern constrained periodic dynamics and equilibria of systems governed by differential inclusions.


49K24 Optimal control problems with differential inclusions (nec./ suff.) (MSC2000)
34G25 Evolution inclusions
47D06 One-parameter semigroups and linear evolution equations
34A60 Ordinary differential inclusions
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