Yuri Nikolaevich Kalinin
70 corp.3, Botanicheskaya st,
Peterhof, Saint-Petersburg,
198516, Russia
Saint-Petersburg State University
postgraduate student
Volker Reitmann
70 corp.3, Botanicheskaya st,
Peterhof, Saint-Petersburg,
198516, Russia
Saint-Petersburg State University
professor of the Department of Applied Cybernetics
Prof. Dr.
We investigate control systems as variational equations in non-standard chains of rigged Hilbert spaces. Monotonicity properties of nonlinearities are introduced with respect to such riggings generated by Lyapunov operators and invariant cones. Sufficient frequency domain conditions for boundedness and the existence of Bohr and Stepanov almost periodic solutions are derived. As an example we consider equations with Duffing-type nonlinearities and almost periodic forcing terms.