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Kiguradze, Ivan Tarielovich

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Total publications: 60
Scientific articles: 49

Number of views:
This page:2311
Abstract pages:6592
Full texts:2986
References:20
Professor
Doctor of physico-mathematical sciences (1973)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 12.01.1937
E-mail: ,
Website: http://www.rmi.acnet.ge/~kig
Keywords: boundary value problems for ordinary differential equations and systems; periodic and bounded solutions; asymptotic of solutions of nonautonomous differential equations; oscillation theory.

Subject:

A method of a priori estimates of solutions of one-sided differential inequalities has been developed, on the basis of which the theory of boundary value problems of Cauchy–Nicoletti, Vallee Poussin, Kneser and periodic type has been constructed for ordinary differential equations and systems with nonintegrable singularities. Optimal existence and uniqueness criteria of periodic and bounded solutions have been established for higher order nonautonomous differential equations. A complete investigation has been carried out of asymptotic properties of solutions of a wide class of nonautonomous differential equations. In particular, the problem on the dimension of the space of vanishing at infinity solutions of a linear homogeneous equation of an arbitrary order has been solved; asymptotic formulas have been obtained for solutions of linear and quasilinear equations; necessary and sufficient conditions have been found for essentially nonlinear equations to have proper, singular, oscillatory and monotone solutions of various types, and asymptotic estimates of these solutions have been established.

Biography

Graduated from Faculty of Mechanics and Mathematics of Tbilisi State University in 1960 (chair of differential and integral equations). Ph.D. thesis was defended in 1963. D.Sci. thesis was defended in 1972. A list of my scientific works contains more than 120 titles. Since 1966 — leader of the Tbilisi seminar on qualitative theory of differential equations. Since 1989 — leader of the seminar on differential equations and mathematical physics at A. Razmadze Mathematical Institute. Since 1994 — managing editor of the "Georgian Mathematical Journal" and chairman of editorial board of the journal "Memoirs on Differential Equations and Mathematical Physics".

In 1975 I was awarded the A. Razmadze prize of the Georgian Academy of Sciences for the monograph "Some singular boundary value problems for ordinary differential equations". In 1979 I was elected a corresponding member of the Georgian Academy of Sciences. Since 1993 I have been a full member (academician) of the Georgian Academy of Sciences.

   
Main publications:
  • Kiguradze I. T., Chanturia T. A. Asymptotic properties of solutions of nonaotonomous ordinary differential equations. Kluwer Academic Publishers, Dordrecht–Boston–London, 1993.
  • Kiguradze I. On periodic solutions of n-th order ordinary differential equations // Nonlinear Anal., 2000, 40(1–8), 309–321.
  • Kiguradze I., Kusano T. On periodic solutions of even-order ordinary differential equations // Ann. Mat. Pura Appl., 2001, 180(3), 285–301.

http://www.mathnet.ru/eng/person17792
List of publications on Google Scholar
http://zbmath.org/authors/?q=ai:kiguradze.ivan-tarielovich
https://mathscinet.ams.org/mathscinet/MRAuthorID/202023

Publications in Math-Net.Ru
2006
1. S. R. Baslandze, I. T. Kiguradze, “On the unique solvability of a periodic boundary value problem for third-order linear differential equations”, Differ. Uravn., 42:2 (2006),  153–158  mathnet  mathscinet; Differ. Equ., 42:2 (2006), 165–171
2004
2. I. T. Kiguradze, S. V. Mukhigulashvili, “On Nonlinear Boundary Value Problems for Two-Dimensional Differential Systems”, Differ. Uravn., 40:6 (2004),  747–755  mathnet  mathscinet; Differ. Equ., 40:6 (2004), 797–806
2003
3. I. T. Kiguradze, “On Boundary Value Problems for Linear Differential Systems with Singularities”, Differ. Uravn., 39:2 (2003),  198–209  mathnet  mathscinet; Differ. Equ., 39:2 (2003), 212–225
2002
4. I. T. Kiguradze, N. L. Partsvaniya, I. P. Stavroulakis, “Oscillatory Properties of Higher-Order Advance Functional-Differential Equations”, Differ. Uravn., 38:8 (2002),  1030–1041  mathnet  mathscinet; Differ. Equ., 38:8 (2002), 1095–1107
2001
5. I. T. Kiguradze, “Blow-Up Kneser Solutions of Nonlinear Higher-Order Differential Equations”, Differ. Uravn., 37:6 (2001),  735–743  mathnet  mathscinet; Differ. Equ., 37:6 (2001), 768–777
2000
6. I. T. Kiguradze, T. Kusano, “Conditions for the existence and uniqueness of periodic solutions of nonautonomous differential equations”, Differ. Uravn., 36:10 (2000),  1301–1306  mathnet  mathscinet; Differ. Equ., 36:10 (2000), 1436–1442
1999
7. I. T. Kiguradze, T. Kusano, “On periodic solutions of higher-order nonautonomous ordinary differential equations”, Differ. Uravn., 35:1 (1999),  72–78  mathnet  mathscinet; Differ. Equ., 35:1 (1999), 71–77
1998
8. I. T. Kiguradze, I. P. Stavroulakis, “On the existence of proper oscillating solutions of advanced differential equations”, Differ. Uravn., 34:6 (1998),  751–757  mathnet  mathscinet; Differ. Equ., 34:6 (1998), 748–754
1997
9. I. T. Kiguradze, “On systems of ordinary differential equations and differential inequalities with multipoint boundary conditions”, Differ. Uravn., 33:5 (1997),  646–652  mathnet  mathscinet; Differ. Equ., 33:5 (1997), 649–655
10. I. T. Kiguradze, B. Puzha, “Theorems of Conti–Opial type for nonlinear functional-differential equations”, Differ. Uravn., 33:2 (1997),  185–194  mathnet  mathscinet; Differ. Equ., 33:2 (1997), 184–193
11. I. T. Kiguradze, Z. P. Sokhadze, “On the Cauchy problem for evolution singular functional-differential equations”, Differ. Uravn., 33:1 (1997),  48–59  mathnet  mathscinet; Differ. Equ., 33:1 (1997), 47–58
1996
12. I. T. Kiguradze, “On a singular Cauchy problem for systems of linear ordinary differential equations”, Differ. Uravn., 32:2 (1996),  171–179  mathnet  mathscinet; Differ. Equ., 32:2 (1996), 173–180
1995
13. I. T. Kiguradze, Z. P. Sokhadze, “On the uniqueness of the solution of the Cauchy problem for functional-differential equations”, Differ. Uravn., 31:12 (1995),  1977–1988  mathnet  mathscinet; Differ. Equ., 31:12 (1995), 1947–1958
1992
14. I. T. Kiguradze, “An oscillation criterion for a class of ordinary differential equations”, Differ. Uravn., 28:2 (1992),  207–219  mathnet  mathscinet  zmath; Differ. Equ., 28:2 (1992), 180–190
1991
15. I. T. Kiguradze, D. I. Chichua, “On the Kneser problem for functional-differential equations”, Differ. Uravn., 27:11 (1991),  1879–1892  mathnet  mathscinet  zmath; Differ. Equ., 27:11 (1991), 1322–1335
1987
16. I. T. Kiguradze, B. L. Shekhter, “Singular boundary value problems for second-order ordinary differential equations”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 30 (1987),  105–201  mathnet  mathscinet  zmath; J. Soviet Math., 43:2 (1988), 2340–2417
17. I. T. Kiguradze, “Boundary value problems for systems of ordinary differential equations”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 30 (1987),  3–103  mathnet  mathscinet  zmath; J. Soviet Math., 43:2 (1988), 2259–2339
1986
18. I. T. Kiguradze, “Periodic solutions of systems of nonautonomous ordinary differential equations”, Mat. Zametki, 39:4 (1986),  562–575  mathnet  mathscinet  zmath; Math. Notes, 39:4 (1986), 308–315  isi
1985
19. D. V. Izyumova, I. T. Kiguradze, “Oscillatory properties of a class of differential equations with deviating argument”, Differ. Uravn., 21:4 (1985),  588–596  mathnet  mathscinet  zmath
20. I. T. Kiguradze, “Solvability of the de la Vallée-Poussin boundary value problem”, Differ. Uravn., 21:3 (1985),  391–398  mathnet  mathscinet  zmath
21. I. T. Kiguradze, “A priori estimates of solutions of higher order nonlinear differential inequalities”, Differ. Uravn., 21:2 (1985),  198–213  mathnet  mathscinet
22. I. T. Kiguradze, “Bounded and periodic solutions of linear differential equations of higher order”, Mat. Zametki, 37:1 (1985),  48–62  mathnet  mathscinet  zmath; Math. Notes, 37:1 (1985), 28–36  isi
1984
23. I. T. Kiguradze, “Behavior of the solutions of higher-order ordinary differential equations in the neighborhood of a singular point”, Differ. Uravn., 20:10 (1984),  1703–1709  mathnet  mathscinet
24. D. G. Bitsadze, I. T. Kiguradze, “Stability of the solution set of nonlinear boundary value problems”, Differ. Uravn., 20:9 (1984),  1495–1501  mathnet  mathscinet
1979
25. I. T. Kiguradze, I. Rahunkova, “Solvability of a nonlinear problem of Kneser's type”, Differ. Uravn., 15:10 (1979),  1754–1765  mathnet  mathscinet  zmath
1977
26. I. T. Kiguradze, “The periodic boundary value problem for a two-dimensional differential system”, Differ. Uravn., 13:6 (1977),  996–1007  mathnet  mathscinet  zmath
1976
27. I. T. Kiguradze, B. Puzha, “Certain boundary value problems for a system of ordinary differential equations”, Differ. Uravn., 12:12 (1976),  2139–2148  mathnet  mathscinet  zmath
1974
28. I. T. Kiguradze, N. R. Lezhava, “Certain nonlinear two-point boundary value problems”, Differ. Uravn., 10:12 (1974),  2147–2161  mathnet  mathscinet  zmath
29. N. V. Gogiberidze, I. T. Kiguradze, “On the question of the disconjugacy of second order singular linear differential equations”, Differ. Uravn., 10:11 (1974),  2064–2067  mathnet  mathscinet  zmath
30. I. T. Kiguradze, “Conditions for the conjugacy of the solutions of nonlinear ordinary differential equations. I, II”, Differ. Uravn., 10:9 (1974),  1586–1594  mathnet  mathscinet  zmath
31. I. T. Kiguradze, “Conditions for the conjugacy of the solutions of nonlinear ordinary differential equations. I, II”, Differ. Uravn., 10:8 (1974),  1387–1399  mathnet  mathscinet  zmath
32. I. T. Kiguradze, N. R. Lezhava, “The problem of the solvability of nonlinear two-point boundary-value problems”, Mat. Zametki, 16:3 (1974),  479–490  mathnet  mathscinet  zmath; Math. Notes, 16:3 (1974), 873–880
1971
33. I. T. Kiguradze, “On the periodic solutions of a system of ordinary differential equations with singularities”, Dokl. Akad. Nauk SSSR, 198:2 (1971),  286–289  mathnet  mathscinet  zmath
34. M. A. Kakabadze, I. T. Kiguradze, “A certain boundary value problem for a system of ordinary differential equations”, Differ. Uravn., 7:9 (1971),  1611–1616  mathnet  mathscinet  zmath
1970
35. I. T. Kiguradze, “A certain singular boundary value problem for an ordinary differential equation of order $n$”, Dokl. Akad. Nauk SSSR, 192:5 (1970),  973–975  mathnet  mathscinet  zmath
36. I. T. Kiguradze, T. A. Chanturiya, “A remark on the asymptotic behavior of the solutions of the equation $u"+a(t)u=0$”, Differ. Uravn., 6:6 (1970),  1115–1117  mathnet  mathscinet  zmath
1969
37. I. T. Kiguradze, “The singular Nicoletti problem”, Dokl. Akad. Nauk SSSR, 186:4 (1969),  769–772  mathnet  mathscinet  zmath
38. I. T. Kiguradze, “The singular two-point boundary value problem”, Differ. Uravn., 5:11 (1969),  2002–2016  mathnet  mathscinet  zmath
39. I. T. Kiguradze, “On monotone solutions of nonlinear ordinary differential equations of order $n$.”, Izv. Akad. Nauk SSSR Ser. Mat., 33:6 (1969),  1373–1398  mathnet  mathscinet  zmath; Math. USSR-Izv., 3:6 (1969), 1293–1317
40. I. T. Kiguradze, “Conditions for non-oscillation of singular linear differential equations of second order”, Mat. Zametki, 6:5 (1969),  633–639  mathnet  mathscinet  zmath; Math. Notes, 6:5 (1969), 843–847
1968
41. I. T. Kiguradze, “Monotonic solutions of $n$th-order nonlinear ordinary differential equations”, Dokl. Akad. Nauk SSSR, 181:5 (1968),  1054–1057  mathnet  mathscinet  zmath
42. I. T. Kiguradze, “Some singular boundary value problems for second order nonlinear ordinary differential equations”, Differ. Uravn., 4:10 (1968),  1753–1773  mathnet  mathscinet  zmath
43. D. V. Izyumova, I. T. Kiguradze, “Some remarks on the solutions of the equation $u"+a(t)f(u)=0$”, Differ. Uravn., 4:4 (1968),  589–605  mathnet  mathscinet
1967
44. I. T. Kiguradze, “A priori estimates for the derivatives of bounded functions satisfying second-order differential inequalities”, Differ. Uravn., 3:7 (1967),  1043–1052  mathnet  mathscinet  zmath
1965
45. I. T. Kiguradze, “On the Cauchy problem for singular systems of ordinary differential equations”, Differ. Uravn., 1:10 (1965),  1271–1291  mathnet  mathscinet  zmath
46. I. T. Kiguradze, “On the question of variability of solutions of nonlinear differential equations”, Differ. Uravn., 1:8 (1965),  995–1006  mathnet  mathscinet  zmath
47. I. T. Kiguradze, “The asymptotic behavior of the solutions of a nonlinear differential equation of Emden–Fowler type”, Izv. Akad. Nauk SSSR Ser. Mat., 29:5 (1965),  965–986  mathnet  mathscinet  zmath
1964
48. I. T. Kiguradze, “On the oscillatory character of solutions of the equation $\frac{d^mu}{dt^m}+a(t)|u|^n\operatorname{sign}u=0$”, Mat. Sb. (N.S.), 65(107):2 (1964),  172–187  mathnet  mathscinet  zmath
1962
49. I. T. Kiguradze, “The capability of certain solutions of ordinary differential equations to oscillate”, Dokl. Akad. Nauk SSSR, 144:1 (1962),  33–36  mathnet  mathscinet  zmath

2010
50. A. V. Arutyunov, Yu. N. Bibikov, F. P. Vasil'ev, I. V. Gaishun, S. V. Emel'yanov, V. A. Il'in, I. T. Kiguradze, S. K. Korovin, L. D. Kudryavtsev, A. B. Kurzhanskii, S. A. Mazanik, E. K. Makarov, A. A. Martynyuk, E. F. Mishchenko, E. I. Moiseev, Yu. S. Osipov, V. A. Pliss, N. Kh. Rozov, V. A. Sadovnichy, A. M. Samoilenko, T. K. Shemjakina, “Nikolai Alekseevich Izobov (A tribute in honor of his 70th birthday)”, Differ. Uravn., 46:1 (2010),  3–8  mathnet  mathscinet  zmath; Differ. Equ., 46:1 (2010), 1–7
2002
51. I. V. Gaishun, N. A. Izobov, V. A. Il'in, I. T. Kiguradze, L. D. Kudryavtsev, V. P. Maksimov, N. Kh. Rozov, T. K. Shemjakina, “N. V. Azbelev (A tribute on the occasion of his 80th birthday)”, Differ. Uravn., 38:7 (2002),  867–869  mathnet  mathscinet; Differ. Equ., 38:7 (2002), 917–919
2000
52. V. N. Abrashin, I. V. Gaishun, V. A. Il'in, I. T. Kiguradze, S. K. Korovin, L. D. Kudryavtsev, A. B. Kurzhanskii, A. A. Martynyuk, V. M. Millionshchikov, Yu. A. Mitropol'skii, V. A. Pliss, N. Kh. Rozov, A. A. Samarskii, A. M. Samoilenko, T. K. Shemjakina, “Nikolai Alekseevich Izobov”, Differ. Uravn., 36:1 (2000),  3–11  mathnet  mathscinet; Differ. Equ., 36:1 (2000), 1–11
1999
53. D. V. Anosov, V. S. Vladimirov, I. V. Gaishun, N. A. Izobov, V. A. Il'in, I. T. Kiguradze, V. A. Kondratiev, L. D. Kudryavtsev, Yu. A. Mitropol'skii, E. F. Mishchenko, O. A. Oleinik, V. A. Pliss, M. I. Rakhimberdiev, N. Kh. Rozov, A. M. Samoilenko, A. F. Filippov, T. K. Shemjakina, “Vladimir Mikhaǐlovich Millionshchikov (on the occasion of his sixtieth birthday)”, Differ. Uravn., 35:10 (1999),  1299–1312  mathnet  mathscinet; Differ. Equ., 35:10 (1999), 1311–1327
1998
54. N. A. Izobov, V. A. Il'in, I. T. Kiguradze, V. A. Kondratiev, A. B. Kurzhanskii, V. M. Millionshchikov, O. A. Oleinik, M. I. Rakhimberdiev, T. K. Shemjakina, “Nikolaǐ Khristovich Rozov (on the occasion of his sixtieth birthday)”, Differ. Uravn., 34:2 (1998),  147–148  mathnet  mathscinet; Differ. Equ., 34:2 (1998), 151–152
1997
55. A. F. Andreev, I. V. Gaishun, V. I. Gromak, N. A. Izobov, V. A. Il'in, I. T. Kiguradze, N. N. Krasovskii, L. D. Kudryavtsev, N. A. Lukashevich, I. P. Martynov, V. A. Pliss, L. A. Cherkas, T. K. Shemjakina, “Nikolaǐ Pavlovich Erugin (on the ninetieth anniversary of his birth)”, Differ. Uravn., 33:5 (1997),  579–582  mathnet  mathscinet; Differ. Equ., 33:5 (1997), 583–586
56. N. A. Izobov, V. A. Il'in, I. T. Kiguradze, L. D. Kudryavtsev, V. P. Maksimov, T. K. Shemjakina, “Nikolaǐ Viktorovich Azbelev (on the occasion of his seventy-fifth birthday)”, Differ. Uravn., 33:4 (1997),  435–439  mathnet  mathscinet; Differ. Equ., 33:4 (1997), 433–438
1995
57. L. M. Berkovich, N. A. Izobov, V. A. Il'in, I. T. Kiguradze, V. A. Pliss, N. Kh. Rozov, “Otakar Boruvka [1899–1995]”, Differ. Uravn., 31:10 (1995),  1770–1771  mathnet  mathscinet; Differ. Equ., 31:10 (1995), 1744–1745
1990
58. N. V. Azbelev, È. I. Grudo, N. A. Izobov, I. T. Kiguradze, V. A. Kondratiev, V. M. Millionshchikov, N. Kh. Rozov, “Obituary: Teǐmuraz Ambros'evich Chanturiya”, Differ. Uravn., 26:12 (1990),  2190–2191  mathnet  mathscinet; Differ. Equ., 26:12 (1990), 1648–1649
1988
59. A. F. Andreev, A. V. Bitsadze, N. P. Erugin, V. I. Zubov, N. A. Izobov, V. A. Il'in, I. T. Kiguradze, N. N. Krasovskii, L. D. Kudryavtsev, V. M. Millionshchikov, V. A. Pliss, A. A. Samarskii, K. S. Sibirskii, A. N. Tikhonov, “Yuriǐ Stanislavovich Bogdanov”, Differ. Uravn., 24:6 (1988),  1091–1097  mathnet  mathscinet  zmath; Differ. Equ., 24:6 (1988), 692–699
1985
60. T. V. Burchuladze, N. P. Vekua, T. G. Gegelia, N. P. Erugin, I. T. Kiguradze, L. D. Kudryavtsev, A. G. Sveshnikov, “Viktor Dmitrievich Kupradze”, Differ. Uravn., 21:11 (1985),  2018–2019  mathnet  mathscinet
1982
61. N. P. Erugin, N. A. Izobov, I. T. Kiguradze, L. D. Kudryavtsev, V. P. Maksimov, “Nikolaǐ Viktorovich Azbelev (on the occasion of his sixtieth birthday)”, Differ. Uravn., 18:4 (1982),  725–730  mathnet  mathscinet  zmath

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