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