E. Iturriaga and H. Leiva, “A Necessary and Sufficient Condition for the Controllability of Linear Systems in Hilbert Spaces and Applications,” IMA Journal of Mathematics, Control and Information, Vol. 25, No. 3, 2008, pp. 269-280.

has been cited by the following article:

• TITLE: A Characterization of Semilinear Surjective Operators and Applications to Control Problems

  AUTHORS: Edgar Iturriaga, Hugo Leiva

  KEYWORDS: Semilinear Surjective Operators, Evolution Equations, Controllability, Damped Wave Equation

  JOURNAL NAME: Applied Mathematics, Vol.1 No.4, October 29, 2010

  ABSTRACT: In this paper we characterize a broad class of semilinear surjective operators given by the following formula where Z are Hilbert spaces, and is a suitable nonlinear function. First, we give a necessary and sufficient condition for the linear operator to be surjective. Second, we prove the following statement: If and is a Lipschitz function with a Lipschitz constant small enough, then and for all the equation admits the following solution .We use these results to prove the exact controllability of the following semilinear evolution equation , , where , are Hilbert spaces, is the infinitesimal generator of strongly continuous semigroup in the control function belong to and is a suitable function. As a particular case we consider the semilinear damped wave equation, the model of vibrating plate equation, the integrodifferential wave equation with Delay, etc.