Electron. J. Diff. Equ., Vol. 2014 (2014), No. 36, pp. 1-15.

Controllability for semilinear functional differential equations without uniqueness

Tran Dinh Ke

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.

Submitted June 27, 2013. Published January 29, 2014.
Math Subject Classifications: 93B05, 93C10, 93C25, 47H04, 47H08, 47H10.
Key Words: Functional differential equation; reachable set; condensing map; non-convex valued multimap; measure of noncompactness; approximate controllability; AR-space; ANR-space; R-delta-map.

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Tran Dinh Ke
Department of Mathematics
Hanoi National University of Education
136 Xuan Thuy, Cau Giay, Hanoi, Vietnam
email: ketd@hnue.edu.vn

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