Volker Reitmann, Saint-Petersburg State University, Department of Mathematics and Mechanics, St. Petersburg, Russia, e-mail: vreitmann@aol.com
Abstract: Realization theory for linear input-output operators and frequency-domain methods for the solvability of Riccati operator equations are used for the stability and instability investigation of a class of nonlinear Volterra integral equations in a Hilbert space. The key idea is to consider, similar to the Volterra equation, a time-invariant control system generated by an abstract ODE in a weighted Sobolev space, which has the same stability properties as the Volterra equation.
Keywords: infinite dimensional Volterra integral equation, realization theory, absolute instability, frequency-domain method
Classification (MSC 2010): 34B16, 34C25
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