Controllability for semilinear functional differential equations without uniqueness

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Controllability for semilinear functional differential equations without uniqueness

Tran Dinh Ke

Electronic journal of differential equations, 01/2014, Volume: 2014, Issue: 36

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We study the controllability for a class of semilinear control problems in Hilbert spaces, for which the uniqueness is unavailable. Using the fixed point theory for multivalued maps with nonconvex values, we show that the nonlinear problem is approximately controllable provided that the corresponding linear problem is. We also obtain some results on the continuity of solution map and the topological structure of the solution set of the mentioned problem.

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