Abstract
The basic methods of the qualitative theory of differential equations are applied to the study of differential equations with discontinuous right-hand sides and differential inclusions. The general properties of trajectories of autonomous systems and the properties of trajectories in a plane (in particular, if there holds only right uniqueness) are described. The existence conditions for bounded and periodic solutions, the methods of studying stability by means of Lyapunov functions and by a first approximation equation are presented.
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© 1988 Springer Science+Business Media Dordrecht
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Filippov, A.F. (1988). Basic Methods of Qualitative Theory. In: Arscott, F.M. (eds) Differential Equations with Discontinuous Righthand Sides. Mathematics and Its Applications, vol 18. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7793-9_4
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DOI: https://doi.org/10.1007/978-94-015-7793-9_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-8449-1
Online ISBN: 978-94-015-7793-9
eBook Packages: Springer Book Archive