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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.
