info@viam.science.tsu.ge (+995 32) 2 30 30 40 (+995 32) 2 18 66 45

Roman Koplatadze

  • Differential Equations and Optimal Control Department
    Senior Researcher
  • Office: room 232, University str.11, 0186 Tbilisi, Georgia
  • Phone: 551515108
  • E-mail: r_koplatadze@yahoo.com roman.koplatadze@tsu.ge
  • Research fields: Ordinary differential equations, Functional differential equations, Qualitative theory of nonautonom

Summary

Education:
1995 - Ph.D, Razmadze Institute of Mathematics of the Georgian Academy of Sciences
1974 - equivalent to a doctor, candidate of physics and mathematics sciences, Iv. Javakhishvili Tbilisi State University
1967-1969 - Aspirant from Iv. Javakhishvili Tbilisi State University
1966 - Graduated specialist in mathematics, Iv. Javakhishvili Tbilisi State University, Faculty of Mechanics and Mathematics
1961-1966 – Iv. Javakhishvili Tbilisi State University, Faculty of Mechanics and Mathematics

Work Experience:
2006- to date Iv. Javakhishvili Tbilisi State University, Department of the Faculty of Exact and Natural Sciences, Associate Professor
TSU, I. Vekua Institute of Applied Mathematics, Senior researcher
1995 – 2006 A. Razmadze Institute of Mathematics of Georgian Academy of Sciences, Leading scientist
1990 - 1995 TSU, I. Vekua Institute of Applied Mathematics , Head of the Department of Differential Equations
1983 - 1990 TSU, I. Vekua Institute of Applied Mathematics, Leading researcher
1970 - 1983 TSU, I. Vekua Institute of Applied Mathematics , Junior researcher

Additional Information
Is the author of more than 135 papers, including 3 monographs. 3 dissertation supervisor. Under his leadership, many master's and bachelor's theses, student projects have been prepared.
Scientific work invited abroad:
2001-2202, Greece, University of Ioannina, reports were prepared and three scientific papers were prepared by Prof. I. With Stavroulak and m. With Gramatikopoulos;
2006, Israel, Samar University, reports were prepared and three scientific papers were prepared by Prof. A.J. With Domoshnitsky.
Scientific grants:
2001, Research Grant of the Greek Ministry of Development within the framework of BilateralS & T Cooperation between the Hellenic Republic and the Republic of Georgia -
University of Ioannina, Department of Mathematics, Ioannina, Greece, Asymptotic behavior of solutions of two-dimensional linear differential systems with deviating
arguments.
2000-2005, Research Grants of the Georgian Academy of Sciences # 1.6.97 # 1.6.00; # 1.6.02;
# 1.6.04. Boundary value problems and asymptotic behavior of solutions of differential equations.
2011-2012, Research Grants of the Shota Rustaveli Georgian National Science Foundation.
Grant No. GNSF / ST09-81-3-101. On asymptotic behavior of solutions of almost linear and essentially nonlinear functional-differential equations.
2013-2014, Research Grants of the Shota Rustaveli Georgian National Science Foundation.
Grant No. 31/09. On asymptotic behavior of solutions of functional differential and discrete equations.
Teaching Courses: Ordinary Differential Equations; Elected Questions of Ordinary Differential
Equations; Functional Differential Equations.
Awards: The Order of Honor I. Javakhishvili Medal of TSU 2022.

Projects

Talks

  • On asymptotic behavior of solutions of higher order Emden-Fowler type difference equations, by Roman Koplatadze (Speaker) at The Fourth International Conference „Modern Problems in Applied Mathematics“ (MPAM2023), Tbilisi, Georgia, 13-16 September, 2023.
  • On Asymptotic Behavior of Solutions of Higher Order Emden-Fowler Type Difference Equations with Deviating Argument, by Roman Koplatadze (Speaker) at The Fourth International Conference "MODERN PROBLEMS IN APPLIED MATHEMATICS", Tbilisi, Georgia, 13-15 September, 2023.
  • ON THE OSCILATORY PROPERTIES OF THE SECOND ORDER EMDENFOWLER TYPE DIFFRENCE EQUATIONS WITH DEVIATING ARGUMENT, by Roman Koplatadze (Speaker) at XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics, Tbilisi, Georgia, 19-22 April, 2023.
  • ON THE OSCILATORY PROPERTIES OF THE SECOND ORDER EMDENFOWLER TYPE DIFFRENCE EQUATIONS WITH DEVIATING ARGUMENT, by Roman Koplatadze (Speaker) at XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics of Ivane Javakhisvili Tbilisi State University, Tbilisi, Georgia, 19-22 April, 2023.
  • Almost Linear Differential Equations , by Roman Koplatadze (Speaker) at 8th Israeli-Czech Workshop on Functional Differential Equations, Ariel, Israeli, 27 August, 2017.
  • On Oscillatory Properties of Solutions of First Order Difference Equations with Several Delay Arguments , by Roman Koplatadze (Speaker) at 6th Ariel Conference on Functional Differential Equations and Applications , Ariel, Israeli, 21-27 August, 2017.
  • Oscillation criteria for higher order functional differential equation , by Roman Koplatadze (Speaker) at XXX Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics , Tbilisi, Georgia, 01 January, 2016.
  • The Specific Properties of Solutions of the First order Differential and difference Equations with Several Delay Arguments, by Roman Koplatadze (Speaker) at Second Tbilisi-Salerno Workshop on Modeling in Mathematics (Tbilisi, Georgia, 2015), Tbilisi, Georgia, 16-18 March, 2015.
  • On Oscillatory Properties of Solutions of Functional Differential Equations , by Roman Koplatadze (Speaker) at International Conference of Differential & Difference Equation and Applications, Ponta Delgada, Portugal, 03-07 September, 2012.
  • Oscillation criteria for higher order nonlinear Functional differential equations , by Roman Koplatadze (Speaker) at International Conference: Continuum Mechanics and Related Problems of Analysis , Tbilisi, Georgia, 09-14 September, 2011.
  • Oscillatory Properties of Solutions of Generalized Emden-Fowler Equations, by Roman Koplatadze (Speaker) at International Conference of Differential & Difference Equation and Applications (Ponta Delgada, Portugal, 2011), Ponta Delgada, Portugal, 04-08 July, 2011.
  • On asymptotic behaviour of solution of nonlinear functional differential equation, by Roman Koplatadze (Speaker) at The 6th International Conference: Dynamical Systems and Applications-2010 (Antalya, Turkey, 2010), Antalya, Turkey, 10-14 July, 2010.
  • ESSENTIALLY NONLINEAR GENERALIZED DIFFERENTIAL EQUATION OF EMDEN-FOWLER TYPE WITH DELAY ARGUMENT, by Roman Koplatadze (Speaker) at XXIII Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics , Tbilisi, Georgia, 22-24 April, 2009.
  • On a singular boundary value problem form the integro-differential equations., by Roman Koplatadze (Speaker) at International Conference on Modern Problems in Applied Mathematics. Dedicated to the 90-th anniversary of Iv. Javakhishvili Tbilisi State University (TSU) and 40-th anniversary of I. Vekua Institute o, Tbilisi, Georgia, 26-28 September, 2008. (poster)
  • Necessary conditions for existence of positive solutions of second order linear differential equation, by Roman Koplatadze (Speaker) at International Conference on Modern Problems in Applied Mathematics. Dedicated to the 90-th anniversary of Iv. Javakhishvili Tbilisi State University (TSU) and 40-th anniversary of I. Vekua Institute o, Tbilisi, Georgia, 26-28 September, 2008.
  • Generalized equation of Emden-Fowler type , by Roman Koplatadze (Speaker) at XXII Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics , Tbilisi, Georgia, 22-24 April, 2008.
  • Quasi-linear functional differential equations with Property A , by Roman Koplatadze (Speaker) at Sixth International ISAAC Congress, Ankara, Turky, 13-18 August, 2007.
  • On oscillatory properties of solutions of generalized Emden- Fowler type differential equations, by Roman Koplatadze (Speaker) at ISAAC Conference on Complex Analysis, Partial Differential Equations, and Mechanics of Continua Dedicated to the Centenary of I. Vekua, Tbilisi, Georgia, 23-27 April, 2007.
  • Generalized Emden-Fowler type nonlinear ordinary differential equations with Property A, by Roman Koplatadze (Speaker) at Fourth International Conference on Differential and Functional Differential Equations (Moscow, 2005), Moscow, Russia, 14-21 August, 2005.
  • , by Roman Koplatadze (Speaker) at International Symposium in Differential Equations and Mathematical Physics , Tbilisi, Georgia, 24-25 December, 2003.
  • Comparison Theorems for Deviated Difference Equations., by Roman Koplatadze (Speaker) at XVI Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics , Tbilisi, Georgia, 01 January, 2002.
  • Oscillatory properties of solutions of two- dimensional linear differential systems with deviated arguments, by Roman Koplatadze (Speaker), Nino Partsvania at XIV Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics , Tbilisi, Georgia, 01 January, 2000.

Publications

  • Roman Koplatadze, Oscillation Criteria for Higher Order Emden-Fowler Type Difference Equations with Delay Argument, I. Vekua Inst. Appl. Math., Rep. 49, Tbilisi State University Press, 2023.
  • Roman Koplatadze, Natia Khachidze, Asymptotic behavior of solutions of n-th order Emden-Fowler difference equations with advanced argument, Journal of Contemporary Mathematical Analysis of Sciences 56, 4, 58-72 , 522, Springer, 2021.
  • Roman Koplatadze, Oscillation criteria for higher order linear differential equations, Proceedings in Mathematics and Statistics V. 379, 206-212., Springer, Singapore, 2021.
  • Roman Koplatadze, Alexander Domoshnitsky, Leonid Berezansky, Oscillation, nonoscillation, stability and asymptotic properties for second and higher order functional differential equations, pages - p. 614, Taylor and Francis Group, 2020.
  • Roman Koplatadze, Oscillation criteria for higher order linear differential equations, Springer Proceedings in Mathematics and Statistics V. 379 (2019), 207-212., Springer, Singapore, 2019.
  • Roman Koplatadze, Alexander Domoshnitsky, On higher order generalized Emden-Fowler differential equation with delay argument, Journal of Mathematical Sciences, Vol. 220, No. 4, 461-482, Springer Science Business Media New York, 2017.
  • Roman Koplatadze, Almost linear functional differential equations with properties A and B, Translations of. Razmadze Math. Inst. 170 , no. 2, 215—242., Elsevier, 2016.
  • Roman Koplatadze, Oscillation criteria for differential equations with several retarded arguments, Funkcialaj Ekvacioj 58, No. 3, 347-364., Elsevier, 2015.
  • Roman Koplatadze, Specific properties of solutions of first order differential equations with several delay arguments, J. Contemporary Math. Anal. 50, No. 5, 229- 2357., Elsevier, 2015.
  • Roman Koplatadze, Oscillation criteria for differential and discrete equations with several delays, Bulletin of TICMI, 18, 10-17, Ivane Javakhishvili Tbilisi State University Press, 2014.
  • Roman Koplatadze, Oscillation criteria for higher order nonlinear functional differential equations with advanced argument, J Math Sci  197, 45–65, Elsevier, 2014.
  • Roman Koplatadze, Alexander Domoshnitsky, On asymptotic behavior of solutions of generalized Emden-Fowler differential equations with delay argument, Abstract and Applied Analysis, Art. ID 168425, 13 pp., Elsevier, 2014.
  • Roman Koplatadze, Oscillation criteria for first order linear difference equations with several delay arguments, Nonlinear Oscillations 17, No. 2, 248-267., Elsevier, 2013.
  • Roman Koplatadze, S. Pinelas, On oscillation of solutions of second order nonlinear difference equations, -Nelīnīĭnī Koliv. 15, no. 2, 194--204, Springer, 2012.
  • Roman Koplatadze, On asymptotic behavior of solutions of n-th order Emden-Fowler differential equations with advanced argument, Czechoslovak Math. J. 60(135), no. 3, 817—833, Elsevier, 2010.
  • Roman Koplatadze, Alexander Domoshnitsky, On a boundary value problem for integro-differential equations on the halfline, Nonlinear Anal. 72, No. 2, 836—846, Elsevier, 2010.
  • Roman Koplatadze, G. Kvinikadze, Necessary conditions for existence of positive solutions of second order linear difference equations and sufficient conditions for oscillation of solutions, Nonlinear oscillations, Springer, 2009.
  • Roman Koplatadze, G. Kvinikadze, Necessary conditions for existence of positive solutions of second order linear difference equations and sufficient conditions for oscillation of solutions., J. Nelīnīĭnī Koliv. 12, No. 2, 180—194, Springer, 2009.
  • Roman Koplatadze, G. Kvinikadze, Necessary conditions for existence of positive solutions of second order linear difference equations and sufficient conditions for oscillation of solutions., Translated from  Nelīnīĭnī Koliv. 12, no. 2, 180—194, Nonlinear Oscil. (N. Y.) 12, no. 2, 184—198, Springer, 2009.
  • Roman Koplatadze, Oscillation criteria for higher order “almost linear” functional differential equation On asymptotic behavior of solutions of almost linear and essentially nonlinear differential equations, Differ. Equ. 16, No. 3, 387—434, Ariel University Center of Samaria, 2009.
  • Roman Koplatadze, Optimal oscillation criteria for first order difference equation with delay argument, Pacific J. Mathematics. 235 (2008), No. 1, 15- 33, Elsevier, 2008.
  • Roman Koplatadze, I. P. Stavroulakis, G. E. Chatzarakis , Optimal oscillation criteria for first order difference equations with delay argument, Pacific Journal of Mathematics 235, No. 1, 15-33, Elsevier, 2008.
  • Roman Koplatadze, Alexander Domoshnitsky, On the Kneser type solutions for two-dimensional linear differential systems with deviating arguments, J. Inequal.  Appl. 330, pp. 22, Springer, 2007.
  • Roman Koplatadze, Nonlinear functional differential equations with Properties A and B, J. Math. Anal.  Appl. 306, 136-160, Elsevier, 2005.
  • Roman Koplatadze, On higher order functional differential equations with Property A, Georgian Math. J. 11, No. 2, 307-336, De Gruyter, 2004.
  • Roman Koplatadze, On the oscillation of solutions of first order differential equations with retarded arguments, Georgian Math. J. 10 (2003), No. 1, 63-76, De Gruyter, 2003.
  • Roman Koplatadze, M. K. Grammatikopoulos, G. Kvinikadze, Linear functional differential equations with Property A., J. Math. Anal. Appl. 284 , No. 1, 294-314, Elsevier, 2003.
  • Roman Koplatadze, Oscillation of second order linear difference equations with deviating arguments, Math. Sci. Appl. 12 (2002), No. 1, 217-226, Department of Mathematical and Physical Sciences Japan Women's University Mejirodai 2-8-1, Bunkyo-ku, 2002.
  • Roman Koplatadze, Comparison theorems for differential equations with several deviations. The case of property B., Mem. Differential Equations Math. Phys. 26, 139-148, Elsevier, 2002.
  • Roman Koplatadze, Oscillation of linear difference equations with deviating arguments, Computers and Mathematics with Appl. 42 , 477-486., Elsevier Science LtD, 2001.
  • Roman Koplatadze, Property A of high order linear differential equations with several deviations, Mem. Differential Equations Math. Phys. 24 , 125-135, Tbilisi University Press, 2001.
  • Roman Koplatadze, Comparison theorems for differential equations with several deviations. The case of property A, Mem. Differential Equations Math. Phys. 24, 115-124, Tbilisi University Press, 2001.