Differential Equations with Impulse Effects (eBook)

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Nikolai A. Perestyuk, Shevchenko Kiev National University, Ukraine; Viktor A. Plotnikov †; Anatolii M. Samoilenko, National Academy of Sciences of Ukraine, Kiev, Ukraine; Nataliya V. Skripnik, Mechnikov Odessa National University, Ukraine.

Introduction 8
Notation 12
Contents 14
1 Impulsive Differential Equations 16
1.1 General Characterization of Systems of Impulsive Differential Equations 16
1.2 Linear Systems 38
2 Impulsive Differential Inclusions 57
2.1 Differential Inclusions with Fixed Times of Pulse Action 57
2.2 Differential Inclusions with Nonfixed Times of Pulse Action 63
2.3 Examples 71
3 Linear Impulsive Differential Inclusions 81
3.1 Statement of the Problem. Theorem on Existence and Uniqueness 81
3.2 Stability of Solutions of Linear Impulsive Differential Inclusions 87
3.3 Periodic Solutions of Linear Impulsive Differential Inclusions 103
3.4 Linear Differential Equations with Pulse Action at Indefinite Times 134
4 Linear Systems with Multivalued Trajectories 139
4.1 Differential Equations with Hukuhara Derivative 139
4.2 Approximation of the Integral Funnel of a Linear Differential Inclusion with the Help of Systems of Differential Equations with Hukuhara Derivative 145
4.3 Linear Differential Equations with p-Derivative 166
4.4 Extension of the Space conv(Rn) for n = 1 170
4.5 Approximation of the Integral Funnel of a Linear Differential Inclusion with the Help of Systems of Differential Equations with p-Derivative 174
5 Method of Averaging in Systems with Pulse Action 184
5.1 Oscillating System with One Degree of Freedom 184
5.2 Systems with Fixed Times of the Pulse Action 209
5.3 Systems with Nonfixed Times of the Pulse Action 219
6 Averaging of Differential Inclusions 235
6.1 Averaging of Inclusionswith Pulses at Fixed Times 235
6.2 Krasnosel’skii–Krein Theorem for Differential Inclusions 244
6.3 Averaging of Inclusions with Pulses at Nonfixed Times 256
6.4 Averaging of Impulsive Differential Equations with Hukuhara Derivative 265
7 Differential Equations with Discontinuous Right-Hand Side 272
7.1 Motions and Quasimotions 272
7.2 Impulsive Motions and Quasimotions 285
7.3 Euler Quasibroken Lines 288
A Some Elements of Set-Valued Analysis 291
B Differential Inclusions 298
References 310
Index 320

lt;P>"This very good book is written by four well-known Ukrainian mathematicians [...]." Mathematical Reviews

"This interesting monograph written by known specialists in the field is addressed to a wide audience such as mathematicians, engineers, biologists and physicists." Zentralblatt für Mathematik