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Abstract

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.

Details

Title
NONLINEAR ANALYSIS AND THE CONTROL OF SPACE WITH PRE-ASSIGNED RESPONSES
Author
MABRY, RICHARD DUVAL
Year
1985
Publisher
ProQuest Dissertations & Theses
ISBN
979-8-205-30782-6
Source type
Dissertation or Thesis
Language of publication
English
ProQuest document ID
303411547
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.