The method of guiding functions (MGF) is one of the tools for solving problems of periodic oscillations in nonlinear systems. In many problems of nonlinear oscillations arises the necessity to use guiding functions which are non-smooth. In particular, such situation appears when different smooth guiding functions are defined in various domains of the phase space of the system. To study these type of problems, for systems admitting forced oscillations, the notion of a non-smooth guiding function and the methods of non-smooth analysis are applied to study oscillation problems in systems governed by differential inclusions. The MGF can be useful not only to justify the existence of oscillations, but also to the study of the qalitative behavior of branches of periodic solutions.
Method of guiding functions in problems of nonlinear analysis / Valeri Obukhovskii;Pietro Zecca;Nguyen Van Loi;Sergei Kornev. - STAMPA. - (2013), pp. 1-177. [10.1007/978-3-642-37070-0]
Method of guiding functions in problems of nonlinear analysis
ZECCA, PIETRO;
2013
Abstract
The method of guiding functions (MGF) is one of the tools for solving problems of periodic oscillations in nonlinear systems. In many problems of nonlinear oscillations arises the necessity to use guiding functions which are non-smooth. In particular, such situation appears when different smooth guiding functions are defined in various domains of the phase space of the system. To study these type of problems, for systems admitting forced oscillations, the notion of a non-smooth guiding function and the methods of non-smooth analysis are applied to study oscillation problems in systems governed by differential inclusions. The MGF can be useful not only to justify the existence of oscillations, but also to the study of the qalitative behavior of branches of periodic solutions.File | Dimensione | Formato | |
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