Krasnosel'skii, Alexander Markovich

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Total publications: 40
Scientific articles: 39

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Doctor of physico-mathematical sciences (1988)
Speciality: 05.13.01 (System analysis, the control and processing of information (separated by fields))
Birth date: 30.04.1955
Keywords: nonlinear analysis, ordinary differential equations, bifurcations, nonlinear resonance, periodic oscillations, hysteresis.


Methods of analysis of degenerated nonlinear operator equations of Hammerstein type with normal linear part were presented. These methods are applicable to the solution of various nonlocal problems on forced oscillations in nonlinear control systems. The theory of periodic oscillations in system with hysteresis was developed. The new method to study Andronov–Hopf bifurcations was presented; the method allow to study variouse degenerate cases and to obtain conditions of existence of cycles and their continua (in collaboration with D. I. Rachinskii). A new class of systems (systems with incomplete corrections) was considered together with Mark Krasnosel'skii and Nikolai Kuznetsov. Various stability conditions of such systems were obtained, these system include so-called "asynchronous systems" as a partial case.


Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1976. Ph.D. thesis (Frequency criteria and harmonic balance method) was defended in 1981, D.Sci. thesis (Methods of analysis of non-local problems for forced oscillations in nonlinear control systems) was defended in 1987, both in the Institute for System Study. Worked in Cardiology center in 1976–1988, then in IITP RAS. A list of my works contains more than 150 titles. Member of Editorial of "Automation and Remote Control", "Pollack periodica" (Hungary), "International Journal of Differential Equations" (Hindawi)

Main publications:
  • Krasnosel'skii A. M. "Asymptotics of nonlinearities and operator equations". Ser. "Operator Theory", vol. 76, Birkhauser, 1995.
  • Krasnosel'skii A. M., Pokrovskii A. V. On subharmonics bifurcation in equations with homogeneous nonlinearities. Discrete and Continuous Dynamical Systems, 7, no. 7, 100–114, 2001.
  • Krasnosel'skii A. M., Mennicken R., Rachinskii D. I. Cycle stability for Hopf bifurcation, generated by sublinear terms. Mathematische Nachrichten, v. 233–234, 171–195, 2002.
  • Krasnosel'skii A. M., Mennicken R., Rachinskii D. I. Small solutions generated by sublinear terms. Journal of Differential Equations, v. 179, 97–132, 2002.
  • Krasnosel'skii A. M., Rachinskii D. I. On a bifurcation governed by hysteresis nonlinearity. Nonlinear Differential Equations and Applications, v. 9, 93–115, 2002.
List of publications on Google Scholar

Publications in Math-Net.Ru
1. A. M. Krasnosel'skii, “A degenerate case of Andronov–Hopf bifurcation at infinity”, Avtomat. i Telemekh., 2010, 11,  55–68  mathnet  mathscinet  zmath; Autom. Remote Control, 71:11 (2010), 2307–2319  isi  scopus
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  mathnet  mathscinet  zmath; Autom. Remote Control, 69:8 (2008), 1297–1310  isi  scopus
3. A. M. Krasnosel'skii, A. V. Pokrovskii, “Dissipativity of a nonresonant pendulum with ferromagnetic friction”, Avtomat. i Telemekh., 2006, 2,  57–69  mathnet  mathscinet  zmath; Autom. Remote Control, 67:2 (2006), 221–232  scopus
4. 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  mathnet  mathscinet  zmath; Funct. Anal. Appl., 39:3 (2005), 194–206  isi  scopus
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  mathnet  mathscinet  zmath; Autom. Remote Control, 65:10 (2004), 1635–1640  isi  scopus
6. 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  mathnet  mathscinet  zmath; Autom. Remote Control, 64:2 (2003), 231–251  isi  scopus
7. A. M. Krasnosel'skii, D. I. Rachinskii, “Continua of Cycles of Higher-Order Equations”, Differ. Uravn., 39:12 (2003),  1605–1616  mathnet  mathscinet; Differ. Equ., 39:12 (2003), 1690–1702
8. 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  mathnet  mathscinet  zmath; Autom. Remote Control, 62:11 (2001), 1783–1802  isi  scopus
9. A. M. Krasnosel'skii, D. I. Rachinskii, “Existence of Continua of Cycles in Hamiltonian Control Systems”, Avtomat. i Telemekh., 2001, 2,  65–74  mathnet  mathscinet  zmath; Autom. Remote Control, 62:2 (2001), 227–235  isi  scopus
10. A. M. Krasnosel'skiĭ, D. I. Rachinskiĭ, “On the Hamiltonicity of Lur'e systems”, Avtomat. i Telemekh., 2000, 8,  25–29  mathnet  mathscinet  zmath; Autom. Remote Control, 61:8 (2000), 1259–1262
11. 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  mathnet  mathscinet  zmath; Autom. Remote Control, 61:6 (2000), 889–903
12. A. M. Krasnosel'skii, V. V. Chernorutski, “Hopf bifurcations generated by small nonlinear terms”, Avtomat. i Telemekh., 1999, 9,  29–35  mathnet  mathscinet  zmath; Autom. Remote Control, 60:9 (1999), 1237–1242  isi
13. A. M. Krasnosel'skii, “Unbounded sequences of cycles in automatic control systems”, Avtomat. i Telemekh., 1999, 8,  74–84  mathnet  mathscinet  zmath; Autom. Remote Control, 60:8 (1999), 1117–1125  isi
14. P. A. Bliman, A. M. Krasnosel'skiĭ, “The Popov criterion in problems of forced oscillations in control systems”, Avtomat. i Telemekh., 1998, 4,  3–14  mathnet  mathscinet  zmath; Autom. Remote Control, 59:4 (1998), 457–466
15. A. M. Krasnosel'skii, “On Forced Oscillation in Systems with Even Unbounded Functional Characteristics”, Avtomat. i Telemekh., 1997, 2,  27–36  mathnet  mathscinet  zmath; Autom. Remote Control, 58:2 (1997), 173–181
16. A. M. Krasnosel'skii, M. A. Krasnosel'skii, “Vector fields in the direct product of spaces, and applications to differential equations”, Differ. Uravn., 33:1 (1997),  60–67  mathnet  mathscinet; Differ. Equ., 33:1 (1997), 59–66
17. P. -A. Bliman, M. Sorin, A. A. Vladimirov, A. M. Krasnosel'skii, “Forced oscillations in control systems with hysteresis”, Dokl. Akad. Nauk, 347:4 (1996),  458–461  mathnet  mathscinet  zmath
18. A. M. Krasnosel'skii, M. Sorin, “Discrete asynchronous iterations”, Avtomat. i Telemekh., 1995, 11,  64–73  mathnet  mathscinet  zmath; Autom. Remote Control, 56:11 (1995), 1557–1564
19. A. M. Krasnosel'skii, “Nonlinear resonance in systems with delay”, Avtomat. i Telemekh., 1995, 2,  14–21  mathnet  mathscinet  zmath; Autom. Remote Control, 56:2 (1995), 160–166
20. A. M. Krasnosel'skiĭ, “Nonresonance sector estimates for nonlinearities in the problem of forced oscillations in control systems”, Avtomat. i Telemekh., 1994, 12,  43–48  mathnet  mathscinet  zmath; Autom. Remote Control, 55:12 (1994), 1740–1744
21. N.. A.. Bobylëv, A. M. Dement'eva, A. M. Krasnosel'skiĭ, “Poincaré's index in problems of control and optimization”, Avtomat. i Telemekh., 1994, 2,  32–38  mathnet  mathscinet  zmath; Autom. Remote Control, 55:2 (1994), 172–177
22. A. M. Krasnosel'skii, M. A. Krasnosel'skii, N. A. Kuznetsov, T. Eirola, O. Nevanlinna, “Iterations with incomplete corrections for linear systems with selfadjoint operators”, Dokl. Akad. Nauk, 338:1 (1994),  35–38  mathnet  mathscinet  zmath
23. A. M. Krasnosel'skii, “On the occurrence of large-amplitude oscillatory regimes in systems with saturation”, Dokl. Akad. Nauk SSSR, 318:4 (1991),  844–848  mathnet  mathscinet  zmath; Dokl. Math., 36:6 (1991), 419–421
24. A. M. Krasnosel'skii, M. A. Krasnosel'skii, N. A. Kuznetsov, “Nonlinear systems with incomplete corrections and their stability”, Dokl. Akad. Nauk SSSR, 318:2 (1991),  291–294  mathnet  mathscinet  zmath; Dokl. Math., 36:5 (1991), 356–357
25. N. A. Bobylev, A. M. Krasnosel'skii, M. Krasnosselsky, “Stability of periodic oscillations and the possibility of obtaining them by the method of harmonic balance”, Avtomat. i Telemekh., 1989, 5,  179–181  mathnet  mathscinet
26. A. M. Krasnosel'skii, “Applicability of features Fredholm theorems in analysis of forced oscillations in nonlinear systems”, Avtomat. i Telemekh., 1988, 12,  162–164  mathnet  mathscinet
27. A. M. Krasnosel'skii, “Directed corrections in the method of harmonic balance”, Dokl. Akad. Nauk SSSR, 294:6 (1987),  1314–1318  mathnet  mathscinet
28. A. M. Krasnosel'skii, “Forced oscillations in systems with hysteresis nonlinearities”, Dokl. Akad. Nauk SSSR, 292:5 (1987),  1078–1082  mathnet  mathscinet  zmath
29. A. M. Krasnosel'skiĭ, “On a class of linear elements with fractional-rational transfer functions”, Avtomat. i Telemekh., 1986, 11,  166–170  mathnet  mathscinet  zmath
30. A. M. Krasnosel'skii, “On Stability of Desynchronized Multi-Component Systems”, Avtomat. i Telemekh., 1985, 11,  170–171  mathnet
31. A. M. Krasnosel'skii, “One-sided estimates in a problem of forced oscillations in nonlinear control systems”, Dokl. Akad. Nauk SSSR, 283:2 (1985),  284–286  mathnet  mathscinet  zmath
32. A. M. Krasnosel'skii, M. A. Krasnosel'skii, “Large amplitude cycles in autonomous systems with hysteresis”, Dokl. Akad. Nauk SSSR, 283:1 (1985),  23–26  mathnet  mathscinet  zmath
33. A. M. Krasnosel'skii, D. I. Petrov, “On periodic oscillations in control systems with delays”, Avtomat. i Telemekh., 1984, 6,  169–171  mathnet  mathscinet  zmath
34. A. M. Krasnosel'skii, “On forced periodic oscillations in the nonlinear systems”, Dokl. Akad. Nauk SSSR, 276:6 (1984),  1356–1359  mathnet
35. A. M. Krasnosel'skii, “Periodic oscillations in complex nonlinear systems”, Avtomat. i Telemekh., 1983, 10,  76–82  mathnet  mathscinet  zmath; Autom. Remote Control, 44:10 (1983), 1301–1306
36. A. M. Krasnosel'skii, “Frequency criteria in the problem of forced oscillations in a control system”, Avtomat. i Telemekh., 1980, 9,  23–30  mathnet  mathscinet
37. A. M. Krasnosel'skii, “New a priori estimates of the solutions of a two-point boundary value problem and their applications”, Sibirsk. Mat. Zh., 21:1 (1980),  115–124  mathnet  mathscinet  zmath; Siberian Math. J., 21:1 (1980), 85–93  isi
38. A. M. Krasnosel'skii, “A priori estimates of the norms of solutions of scalar inequalities”, Dokl. Akad. Nauk SSSR, 243:5 (1978),  1119–1122  mathnet  mathscinet  zmath
39. A. M. Krasnosel'skii, “Remarks on the fixed points of monotone operators”, Uspekhi Mat. Nauk, 32:6(198) (1977),  257–258  mathnet  mathscinet  zmath

40. 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  mathnet

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