Approximate controllability of semilinear functional equations in Hilbert spaces

Dauer J., Mahmudov N.

Journal of Mathematical Analysis and Applications, vol.273, no.2, pp.310-327, 2002 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 273 Issue: 2
  • Publication Date: 2002
  • Doi Number: 10.1016/s0022-247x(02)00225-1
  • Journal Name: Journal of Mathematical Analysis and Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.310-327
  • Keywords: Approximate controllability, Banach fixed point theorem, Complete controllability, Schauder fixed point theorem, Semilinear functional equations, Weak approximate controllability
  • Open Archive Collection: Article
  • Azerbaijan State University of Economics (UNEC) Affiliated: No

Abstract

In this paper approximate and complete controllability for semilinear functional differential systems is studied in Hilbert spaces. Sufficient conditions are established for each of these types of controllability. The results address the limitation that linear systems in infinite-dimensional spaces with compact semigroup cannot be completely controllable. The conditions are obtained by using the Schauder fixed point theorem when the semigroup is compact and the Banach fixed point theorem when the semigroup is not compact. © 2002 Elsevier Science (USA). All rights reserved.