Abstract/Details

NONLINEAR ANALYSIS AND THE CONTROL OF SPACE WITH PRE-ASSIGNED RESPONSES

MABRY, RICHARD DUVAL. 
 University of South Florida ProQuest Dissertations Publishing,  1985. 8607187.

Abstract (summary)

Nonlinear control systems of the type: (C) x' + A(t)x = B(t)u, t (ELEM) 0,T , and nonlinear operator equations of the type: (E) Au - (lamda) Tu + (mu) Cu = f are studied. It is shown that the system (C) can be controlled in Banach spaces with responses x(t) from known classes of functions, although the associated Cauchy problem might not be solvable by existing evolution theories.

It is also shown that (E) is solvable in separable Hilbert spaces if the operators A, T and C are, at least, monotone, positive compact and homogeneous compact, respectively. The symbols (lamda),(mu) denote real parameters. Recent results of Kesavan are thus extended. While Kesavan used Galerkin approximations, degree-theoretic arguments are employed in this work.

Various examples are given illustrating the theory.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences
Title
NONLINEAR ANALYSIS AND THE CONTROL OF SPACE WITH PRE-ASSIGNED RESPONSES
Author
MABRY, RICHARD DUVAL
Number of pages
76
Degree date
1985
School code
0206
Source
DAI-B 47/01, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
979-8-205-30782-6
University/institution
University of South Florida
University location
United States -- Florida
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
8607187
ProQuest document ID
303411547
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/303411547