01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date:
01.03.1969
E-mail:
,
Keywords:
nonlinear analysis,
systems with hysteresis,
periodic solutions of differential equations,
Hopf bifurcation,
fixed point principles,
monotone operators.
Main publications:
Krasnosel'skii M. A., Mennicken R., Rachinskii D. I. Potential bounds in problems on quasilinear elliptic equations // Math. Nachr., 1999, 207, 133–155.
Rachinskii D. I. Asymptotic stability of large-amplitude oscillations in systems with hysteresis // NoDEA Nonlinear Differential Equations Appl., 1999, 6(3), 267–288.
Pavel Gurevich, Dmitrii Rachinskii, “Well-posedness of parabolic equations containing hysteresis with diffusive thresholds”, Tr. Mat. Inst. Steklova, 283 (2013), 92–114; Proc. Steklov Inst. Math., 283 (2013), 87–109
2008
2.
A. M. Krasnosel'skii, D. I. Rachinskii, “Criteria of resonance origin in a single-circuit control system with saturation”, Avtomat. i Telemekh., 2008, 8, 33–47; Autom. Remote Control, 69:8 (2008), 1297–1310
2005
3.
A. M. Krasnosel'skii, D. I. Rachinskii, “On the Number of Unbounded Solution Branches in a Neighborhood of an Asymptotic Bifurcation Point”, Funktsional. Anal. i Prilozhen., 39:3 (2005), 37–53; Funct. Anal. Appl., 39:3 (2005), 194–206
2004
4.
D. I. Rachinskii, “On bifurcation of large-amplitude stable cycles for equations with hysteresis”, Avtomat. i Telemekh., 2004, 12, 62–84; Autom. Remote Control, 65:12 (2004), 1915–1937
5.
A. M. Krasnosel'skii, A. V. Pokrovskii, D. I. Rachinskii, “Guaranteed convergence rate estimates for a class of iterative procedures: their comparison”, Avtomat. i Telemekh., 2004, 10, 128–133; Autom. Remote Control, 65:10 (2004), 1635–1640
2003
6.
D. I. Rachinskii, “On Natural Continua of Periodic Solutions of the Systems with Hysteresis”, Avtomat. i Telemekh., 2003, 3, 84–103; Autom. Remote Control, 64:3 (2003), 420–438
7.
A. M. Krasnosel'skii, D. I. Rachinskii, “On a Nonlocal Condition for Existence of Cycles of Hysteresis Systems”, Avtomat. i Telemekh., 2003, 2, 66–87; Autom. Remote Control, 64:2 (2003), 231–251
8.
A. M. Krasnosel'skii, D. I. Rachinskii, “Continua of Cycles of Higher-Order Equations”, Differ. Uravn., 39:12 (2003), 1605–1616; Differ. Equ., 39:12 (2003), 1690–1702
2001
9.
P.-A. Bliman, A. M. Krasnosel'skii, D. I. Rachinskii, “On Strong Resonance under Bifurcations in Control Systems”, Avtomat. i Telemekh., 2001, 11, 29–50; Autom. Remote Control, 62:11 (2001), 1783–1802
10.
A. M. Krasnosel'skii, D. I. Rachinskii, “Existence of Continua of Cycles in Hamiltonian Control Systems”, Avtomat. i Telemekh., 2001, 2, 65–74; Autom. Remote Control, 62:2 (2001), 227–235
2000
11.
A. M. Krasnosel'skiĭ, D. I. Rachinskiĭ, “On the Hamiltonicity of Lur'e systems”, Avtomat. i Telemekh., 2000, 8, 25–29; Autom. Remote Control, 61:8 (2000), 1259–1262
12.
P. A. Bliman, A. M. Krasnosel'skiĭ, D. I. Rachinskiĭ, “Sector estimates for nonlinearities and the existence of auto-oscillations in control systems”, Avtomat. i Telemekh., 2000, 6, 3–18; Autom. Remote Control, 61:6 (2000), 889–903
1998
13.
D. I. Rachinskiĭ, “Equivalent combinations of supports”, Avtomat. i Telemekh., 1998, 10, 24–34; Autom. Remote Control, 59:10 (1998), 1370–1378
1997
14.
M. A. Krasnosel'skii, N. A. Kuznetsov, R. Mertz, D. I. Rachinskii, “Iterative Procedures with Incomplete Corrections and Solution of Nonlinear Equations”, Avtomat. i Telemekh., 1997, 8, 46–56; Autom. Remote Control, 58:8 (1997), 1285–1293
15.
D. I. Rachinskii, “On the Cauchy problem for differential equations with Mroz hysteresis nonlinearity”, Differ. Uravn., 33:8 (1997), 1041–1048; Differ. Equ., 33:8 (1997), 1047–1054
1996
16.
M. A. Krasnosel'skii, N. A. Kuznetsov, D. I. Rachinskii, “Nonlinear Potential Systems with Incomplete Corrections”, Avtomat. i Telemekh., 1996, 7, 11–17; Autom. Remote Control, 57:7 (1996), 918–924
1995
17.
D. I. Rachinskii, “Forced oscillations in control systems under near-resonance conditions”, Avtomat. i Telemekh., 1995, 11, 87–98; Autom. Remote Control, 56:11 (1995), 1575–1584
1994
18.
M. A. Krasnosel'skiĭ, D. I. Rachinskiĭ, “Invariant convex classes of states of continual relay systems”, Avtomat. i Telemekh., 1994, 10, 17–26; Autom. Remote Control, 55:10 (1994), 1405–1412
19.
M. A. Krasnosel'skiĭ, A. V. Pokrovskiĭ, D. I. Rachinskii, I. D. Mayergoyz, “Operators of hysteresis nonlinearities generated by continual relay systems”, Avtomat. i Telemekh., 1994, 7, 49–60; Autom. Remote Control, 55:7 (1994), 964–973
20.
D. I. Rachinskii, “Transition to normal states in general continual relay systems”, Dokl. Akad. Nauk, 338:4 (1994), 457–460; Dokl. Math., 50:2 (1995), 287–291
1993
21.
M. A. Krasnosel'skii, I. D. Mayergoyz, A. V. Pokrovskii, D. I. Rachinskii, “Differential equations with hysteresis nonlinearities of vector
relay systems type”, Dokl. Akad. Nauk, 331:4 (1993), 398–400; Dokl. Math., 48:1 (1994), 105–109
22.
M. A. Krasnosel'skii, D. I. Rachinskii, “Normal states of vector relay systems”, Dokl. Akad. Nauk, 330:5 (1993), 556–558; Dokl. Math., 47:3 (1993), 577–580
23.
M. A. Krasnosel'skii, I. D. Mayergoyz, A. V. Pokrovskii, D. I. Rachinskii, “Variable states of continual relay systems”, Dokl. Akad. Nauk, 330:4 (1993), 427–429; Dokl. Math., 47:3 (1993), 513–517
1992
24.
A. V. Pokrovskiĭ, D. I. Rachinskiĭ, “Nonexistence of weakly improving monotone shifts in semi-ordered sets with nontrivial topological struc”, Avtomat. i Telemekh., 1992, 12, 155–158; Autom. Remote Control, 53:12 (1992), 1957–1959
1991
25.
D. I. Rachinskiĭ, “Singular points of point mappings”, Avtomat. i Telemekh., 1991, 12, 158–161; Autom. Remote Control, 52:12 (1991), 1769–1771
1998
26.
E. A. Asarin, I. A. Bakhtin, N. A. Bobylev, V. A. Bondarenko, V. Sh. Burd, E. A. Gorin, S. V. Emel'yanov, P. P. Zabreiko, L. A. Ivanov, V. S. Kozyakin, A. M. Krasnosel'skii, N. A. Kuznetsov, A. B. Kurzhanskii, A. Yu. Levin, È. M. Muhamadiev, A. I. Perov, Yu. V. Pokornyi, A. V. Pokrovskii, D. I. Rachinskii, V. V. Strygin, Ya. Z. Tsypkin, V. V. Chernorutski, “Memory of M. A. Krasnosel'skii”, Avtomat. i Telemekh., 1998, 2, 179–184
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