Electronic Journal of Differential Equations,
Vol. 2014 (2014), No. 36, pp. 1-15.
Title: Controllability for semilinear functional differential equations
without uniqueness
Author: Tran Dinh Ke (Hanoi National Univ. of Education, Vietnam)
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.