Publications

• 2023

  ČERMÁK, J.; FEDORKOVÁ, L. On a Nearly Forgotten Polynomial Result by P. Bohl. AMERICAN MATHEMATICAL MONTHLY, 2023, vol. 130, no. 2, p. 176-181. ISSN: 0002-9890.
  Detail | WWW | Full text in the Digital Library

  KISELA, T.; ČERMÁK, J. Stabilization and destabilization of fractional oscillators via a delayed feedback control. Communications in Nonlinear Science and Numerical Simulation, 2023, vol. 117, no. 1, p. 1-16. ISSN: 1007-5704.
  Detail | WWW

  ČERMÁK, J.; KISELA, T.; NECHVÁTAL, L. The Lambert function method in qualitative analysis of fractional delay differential equations. Fractional Calculus and Applied Analysis, 2023, vol. 26, no. 4, p. 1545-1565. ISSN: 1311-0454.
  Detail | WWW | Full text in the Digital Library

• 2022

  ČERMÁK, J.; NECHVÁTAL, L. On stability of linear differential equations with commensurate delayed arguments. APPLIED MATHEMATICS LETTERS, 2022, vol. 125, no. 1, p. 1-8. ISSN: 0893-9659.
  Detail | WWW

  ČERMÁK, J.; FEDORKOVÁ, L.; KUREŠ, M. Complete classification scheme for the distribution of trinomial zeros with respect to their moduli. Publicationes Mathematicae Debrecen, 2022, vol. 101, no. 1-2, p. 119-146. ISSN: 0033-3883.
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• 2021

  ČERMÁK, J.; NECHVÁTAL, L. On a problem of linearized stability for fractional difference equations. NONLINEAR DYNAMICS, 2021, vol. 104, no. 2, p. 1253-1267. ISSN: 1573-269X.
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• 2020

  ČERMÁK, J.; KISELA, T.; NECHVÁTAL, L. Několik poznámek ke zlomkovému kalkulu. Pokroky matematiky, fyziky a astronomie, 2020, vol. 65, no. 3, p. 157-175. ISSN: 0032-2423.
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  ČERMÁK, J.; NECHVÁTAL, L. On stabilization of unstable steady states of autonomous ordinary differential equations via delayed feedback controls. PHYSICA D-NONLINEAR PHENOMENA, 2020, vol. 404, no. 1, p. 1-30. ISSN: 0167-2789.
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  ČERMÁK, J.; NECHVÁTAL, L. On exact and discretized stability of a linear fractional delay differential equation. APPLIED MATHEMATICS LETTERS, 2020, vol. 105, no. 1, p. 1-9. ISSN: 0893-9659.
  Detail | WWW

• 2019

  KISELA, T.; ČERMÁK, J. Oscillatory and asymptotic properties of fractional delay differential equations. Electronic Journal of Differential Equations, 2019, vol. 2019, no. 33, p. 1-15. ISSN: 1072-6691.
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  KISELA, T.; ČERMÁK, J. Delay-dependent stability switches in fractional differential equations. Communications in Nonlinear Science and Numerical Simulation, 2019, vol. 79, no. 1, p. 1-19. ISSN: 1007-5704.
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  ČERMÁK, J.; NECHVÁTAL, L. Stability and chaos in the fractional Chen system. Chaos, Solitons & Fractals, 2019, vol. 125, no. 1, p. 24-33. ISSN: 0960-0779.
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  ČERMÁK, J.; JÁNSKÝ, J.; NECHVÁTAL, L. Exact versus discretized stability regions for a linear delay differential equation. APPLIED MATHEMATICS AND COMPUTATION, 2019, vol. 347, no. 1, p. 712-722. ISSN: 0096-3003.
  Detail | WWW

• 2018

  ČERMÁK, J.; JÁNSKÝ, J.; MATSUNAGA, H. On stability and stabilization of some discrete dynamical systems. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, vol. 41, no. 10, p. 3684-3695. ISSN: 0170-4214.
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  ČERMÁK, J.; NECHVÁTAL, L. Local Bifurcations and Chaos in the Fractional Rössler System. International Journal of Bifurcations & Chaos, 2018, vol. 28, no. 8, p. 1850098-1 (1850098-17 p.)ISSN: 0218-1274.
  Detail | WWW

• 2017

  ČERMÁK, J.; KISELA, T.; DOŠLÁ, Z. Fractional differential equations with a constant delay: Stability and asymptotics of solutions. APPLIED MATHEMATICS AND COMPUTATION, 2017, vol. 298, no. 1, p. 336-350. ISSN: 0096-3003.
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  ČERMÁK, J.; NECHVÁTAL, L. The Routh–Hurwitz conditions of fractional type in stability analysis of the Lorenz dynamical system. NONLINEAR DYNAMICS, 2017, vol. 87, no. 2, p. 939-954. ISSN: 1573-269X.
  Detail | WWW

• 2016

  ČERMÁK, J.; KISELA, T.; HORNÍČEK, J. Stability regions for fractional differential systems with a time delay. Communications in Nonlinear Science and Numerical Simulation, 2016, vol. 31, no. 1-3, p. 108-123. ISSN: 1007-5704.
  Detail | WWW

  ČERMÁK, J.; JÁNSKÝ, J. Stability and periodic investigations of linear planar difference systems. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2016, vol. 39, no. 18, p. 5343-5354. ISSN: 0170-4214.
  Detail | WWW

• 2015

  KISELA, T.; ČERMÁK, J. Stability properties of two- term fractional differential equations. NONLINEAR DYNAMICS, 2015, vol. 80, no. 4, p. 1673-1684. ISSN: 0924- 090X.
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  ČERMÁK, J. Stability conditions for linear delay difference equations: A survey and perspectives. Tatra Mountains Mathematical Publications, 2015, vol. 63, no. 63, p. 1-29. ISSN: 1210-3195.
  Detail | WWW

  ČERMÁK, J.; JÁNSKÝ, J. Explicit stability conditions for a linear trinomial delay difference equation. APPLIED MATHEMATICS LETTERS, 2015, vol. 43, no. 5, p. 56-60. ISSN: 0893- 9659.
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  ČERMÁK, J.; DRAŽKOVÁ, J. On stability sets for numerical discretizations of neutral delay differential equations. Tatra Mountains Mathematical Publications, 2015, vol. 63, no. 2, p. 89-100. ISSN: 1210-3195.
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  KISELA, T.; ČERMÁK, J. Asymptotic Stability Of Dynamic Equations With Two Fractional Terms: Continuous Versus Discrete Case. Fractional Calculus and Applied Analysis, 2015, vol. 18, no. 2, p. 437-458. ISSN: 1311-0454.
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  ČERMÁK, J.; NECHVÁTAL, L. O rozložení kořenů kubického polynomu. Kvaternion, 2015, vol. 2015, no. 1- 2, p. 25-39. ISSN: 1805- 1324.
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  ČERMÁK, J.; NECHVÁTAL, L.; GYŐRI, I. On explicit stability conditions for a linear fractional difference system. Fractional Calculus and Applied Analysis, 2015, vol. 18, no. 3, p. 651-672. ISSN: 1311-0454.
  Detail | WWW

  ČERMÁK, J.; JÁNSKÝ, J.; TOMÁŠEK, P. Two types of stability conditions for linear delay difference equations. APPL ANAL DISCR MATH, 2015, vol. 9, no. 4, p. 120-138. ISSN: 1452- 8630.
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• 2014

  ČERMÁK, J.; HRABALOVÁ, J. Delay- dependent stability criteria for neutral delay differential and difference equations. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2014, vol. 34, no. 11, p. 4577-4588. ISSN: 1078- 0947.
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  ČERMÁK, J.; JÁNSKÝ, J. On a generalization of the Levin- May Theorem. Carpathian Journal of Mathematics, 2014, vol. 30, no. 1, p. 55-62. ISSN: 1584- 2851.
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  ČERMÁK, J.; KISELA, T. Introduction to Stability Theory of Linear Fractional Difference Equations. In Fractional Calculus: Theory. Mathematics Research Developments. 2014. p. 117-162. ISBN: 978-1-63463-002- 3.
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  ČERMÁK, J.; JÁNSKÝ, J. Stability switches in linear delay difference equations. APPLIED MATHEMATICS AND COMPUTATION, 2014, vol. 243, no. 9, p. 755-766. ISSN: 0096- 3003.
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  ČERMÁK, J.; KISELA, T. Exact and discretized stability of the Bagley- Torvik equation. Journal of Computational and Applied Mathematics, 2014, vol. 269, no. 10, p. 53-67. ISSN: 0377- 0427.
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  ČERMÁK, J.; TOMÁŠEK, P. On delay-dependent stability conditions for a three- term linear difference equation. Funkcialaj Ekvacioj Serio Internacia, 2014, vol. 57, no. 1, p. 91-106. ISSN: 0532- 8721.
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  ČERMÁK, J.; JÁNSKÝ, J. Elementární důkaz Levinovy- Mayovy věty. Kvaternion, 2014, vol. 2, no. 2, p. 57-68. ISSN: 1805- 1324.
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  ČERMÁK, J.; DRAŽKOVÁ, J. On stability regions for some delay differential equations and their discretizations. Periodica Mathematica Hungarica, 2014, vol. 68, no. 2, p. 193-206. ISSN: 0031- 5303.
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• 2013

  ČERMÁK, J.; KISELA, T.; NECHVÁTAL, L. Stability regions for linear fractional differential systems and their discretizations. APPLIED MATHEMATICS AND COMPUTATION, 2013, vol. 219, no. 12, p. 7012-7022. ISSN: 0096- 3003.
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  ČERMÁK, J. Some qualitative properties of linear dynamic equations with multiple delays. Advances in Difference Equations, 2013, vol. 2013, no. 2013, p. 1-12. ISSN: 1687- 1847.
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• 2012

  ČERMÁK, J.; DVOŘÁKOVÁ, S. Boundedness and asymptotic properties of solutions of some linear and sublinear delay difference equations. APPLIED MATHEMATICS LETTERS, 2012, vol. 25, no. 2, p. 813-817. ISSN: 0893- 9659.
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  ČERMÁK, J.; JÁNSKÝ, J.; TOMÁŠEK, P. On necessary and sufficient conditions for the asymptotic stability of higher order linear difference equations. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2012, vol. 18, no. 11, p. 1781-1800. ISSN: 1023- 6198.
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  ČERMÁK, J.; KISELA, T.; NECHVÁTAL, L. Stability and asymptotic properties of a linear fractional difference equation. Advances in Difference Equations, 2012, vol. 2012, no. 1, p. 1-14. ISSN: 1687-1847.
  Detail | WWW | Full text in the Digital Library

• 2011

  ČERMÁK, J. The stability and asymptotic properties of the Theta- methods for the pantograph equation. IMA Journal of Numerical Analysis, 2011, vol. 31, no. 4, p. 1533-1551. ISSN: 0272- 4979.
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  ČERMÁK, J.; KISELA, T.; NECHVÁTAL, L. Discrete Mittag- Leffler functions in linear fractional difference equations. Abstract and Applied Analysis, 2011, vol. 2011, no. 2011, p. 1-21. ISSN: 1085- 3375.
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• 2010

  ČERMÁK, J. On a linear difference equation with several infinite lags. Fasciculi Mathematici, 2010, vol. 2010, no. 44, p. 19-28. ISSN: 0044- 4413.
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  ČERMÁK, J. Asymptotic bounds for linear difference systems. Advances in Difference Equations, 2010, vol. 2010, no. 2010, p. 1-14. ISSN: 1687- 1839.
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  ČERMÁK, J.; NECHVÁTAL, L. On (q,h) - analogue of fractional calculus. JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2010, vol. 17, no. 1, p. 1-18. ISSN: 1402- 9251.
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  ČERMÁK, J.; KISELA, T. Note on a discretization of a linear fractional differential equation. Mathematica Bohemica, 2010, vol. 135, no. 2, p. 179-188. ISSN: 0862- 7959.
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• 2009

  ČERMÁK, J. The asymptotic behaviour of q - difference equations with multiple delays. Tatra Mountains Mathematical Publications, 2009, vol. 2009, no. 43, p. 41-50. ISSN: 1210- 3195.
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  ČERMÁK, J.; JÁNSKÝ, J. On the asymptotics of the trapezoidal rule for the pantograph equation. Mathematics of Computation, 2009, vol. 78, no. 268, p. 2107-2126. ISSN: 0025- 5718.
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  ČERMÁK, J. The differential equation with a power delay and its numerical discretizations. International Journal of Qualitative Theory of Differential Equations and Applications, 2009, vol. 2, no. 1, p. 24-32. ISSN: 0973- 3590.
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• 2008

  ČERMÁK, J.; KUNDRÁT, P.; URBÁNEK, M. Delay equations on time scales: Essentials and asymptotics of solutions. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2008, vol. 14, no. 6, p. 567-580. ISSN: 1023- 6198.
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  ČERMÁK, J. On the differential and difference equation with a power delayed argument. Electronic Journal of Qualitative Theory of Differential Equations, 2008, vol. 2008, no. 5, p. 1-8. ISSN: 1417- 3875.
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  ČERMÁK, J.; DVOŘÁKOVÁ, S. Asymptotic estimation for some nonlinear delay differential equations. Results in Mathematics, 2008, vol. 51, no. 3- 4, p. 201-213. ISSN: 1422- 6383.
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  ČERMÁK, J. On the differential equation with power coefficients and proportional delays. Tatra Mountains Mathematical Publications, 2008, vol. 2007, no. 38, p. 57-69. ISSN: 1210- 3195.
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• 2007

  ČERMÁK, J. On a linear differential equation with a proportional delay. Mathematische Nachrichten, 2007, vol. 280, no. 5- 6, p. 495-504. ISSN: 0025- 584X.
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  ČERMÁK, J. Transformations and canonical forms for delay dynamic equations. In Folia FSN Universitatis Masarykianae Brunensis, Mathematica. Brno: Masarykova univerzita, 2007. p. 59-66.
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  ČERMÁK, J.; URBÁNEK, M. On the asymptotics of solutions of delay dynamic equations on time scales. MATHEMATICAL AND COMPUTER MODELLING, 2007, vol. 46, no. 3- 4, p. 445-458. ISSN: 0895- 7177.
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  ŠLAPAL, J.; ČERMÁK, J. Classical and Fractional Mathematical Approaches to Modern Control Theory. In Simulation Modelling of Mechatronic Systems III. mechatronics. Brno: Brno University of Technology, Faculty of Mechanical Engineering, 2007. p. 3-14. ISBN: 978-80-214-3559- 9.
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• 2006

  ČERMÁK, J.; URBÁNEK, M. The asymptotic properties of the dynamic equation with a delayed argument. Opuscula Mathematica, 2006, vol. 26, no. 3, p. 421-429. ISSN: 1232- 9274.
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  ČERMÁK, J. On matrix differential equations with several unbounded delays. European Journal of Applied Mathematics, 2006, vol. 17, no. 7, p. 417-433. ISSN: 0956- 7925.
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  ŠLAPAL, J.; ČERMÁK, J. Modern Mathematical Methods in Control Theory. In Simulation Modelling of Mechatronic Systems II. mechatronics. Brno: Brno University of Technology, 2006. p. 3-13. ISBN: 80-214-3341- 8.
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• 2005

  ČERMÁK, J. A Differential and Difference Equation with a Constant Delay. In Proceedings of the Eighth International Conference on Difference Equations and Applications. Boca Raton, FL, USA: Chapman & Hall/ CRC, 2005. p. 75 ( p.)ISBN: 1-58488-536- X.
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  Šlapal, J., Čermák, J. Modern Methods of Mathematical Modelling of System Control. In Modelling of Mechatronics Systems I. Fakulta strojního inženýrství. Brno: Vysoké učení technické v Brně, 2005. p. 1-10. ISBN: 80-214-3144- X.
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  ČERMÁK, J., KUNDRÁT, P. On the discretized pantograph equation. Inženýrská mechanika - Engineering Mechanics, 2005, vol. 12, no. A1, p. 203-210. ISSN: 1210- 2717.
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  ČERMÁK, J. On the related asymptotics of delay differential and difference equations. Dynamic systems and applications, 2005, vol. 14, no. 3 & 4, p. 419 ( p.)ISSN: 1056- 2176.
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  ČERMÁK, J. Asymptotic properties of differential systems with unbounded delays. In 2004 - Dynamical systems and applications. Delhi (India): GBS Publishers & Distributors (India), 2005. p. 195 ( p.)ISBN: 81-89476-00- 9.
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• 2004

  ČERMÁK, J., KUNDRÁT, P. Linear differential equations with unbounded delays and a forcing term. Abstract and Applied Analysis, 2004, vol. 2004, no. 4, p. 337 ( p.)ISSN: 1085- 3375.
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  ČERMÁK, J. The Schröder equation and asymptotic properties of linear delay differential equations. Electronic Journal of Qualitative Theory of Differential Equations, 2004, vol. 2004, no. 6, p. 1 ( p.)ISSN: 1417- 3875.
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  ČERMÁK, J. Difference equations in the qualitative theory of delay differential equations. In New Progress in Difference Equations. Boca Raton, Florida, USA: Chapman & Hall/ CRC, 2004. p. 391 ( p.)ISBN: 0-415-31675- 8.
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• 2003

  ČERMÁK, J. The asymptotic of solutions for a class of delay differential equations. Rocky Mountain Journal of Mathematics, 2003, vol. 33, no. 3, p. 775 ( p.)ISSN: 0035- 7596.
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• 2002

  ČERMÁK, J. A change of variables for differential equations with deviating arguments. In Colloquium on Differential and Difference equations. Brno: Masarykova univerzita Brno, 2002. p. 87 ( p.)ISBN: 80-210-0536- X.
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  ČERMÁK, J. The Abel equation in the asymptotic theory of functional differential equations. AEQUATIONES MATHEMATICAE, 2002, vol. 64, no. 3, p. 89 ( p.)ISSN: 0001- 9054.
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  ČERMÁK, J. A change of variables in the asymptotic theory of differential equations with unbounded delays. Journal of Computational and Applied Mathematics, 2002, vol. 143, no. 6, p. 81 ( p.)ISSN: 0377- 0427.
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• 2001

  ČERMÁK, J. Linear differential systems with an unbounded delay. 2001, vol. 13, no. 9, p. 33 ( p.)ISSN: 80-7100-817- 6.
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• 2000

  ČERMÁK, J. Asymptotic behaviour of solutions of some differential equations with an unbounded delay. Electronic Journal of Qualitative Theory of Differential Equations, 2000, vol. 2000, no. 2, p. 1 ( p.)ISSN: 1417- 3875.
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  ČERMÁK, J. Asymptotic behaviour of solutions of some linear delay differential equations. Mathematica Bohemica, 2000, vol. 125, no. 3, p. 355 ( p.)ISSN: 0862- 7959.
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  ČERMÁK, J. Asymptotic properties of differential equations with advanced argument. Czechoslovak Mathematical Journal, 2000, vol. 125, no. 50, p. 825 ( p.)ISSN: 0011- 4642.
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  ČERMÁK, J. Linear differential equations with several unbounded delays. ARCHIVUM MATHEMATICUM, 2000, vol. 36, no. 12, p. 421 ( p.)ISSN: 0044- 8753.
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  ČERMÁK, J. Note on canonical forms for functional differential equations. Mathematica Pannonica, 2000, vol. 11, no. 1, p. 29 ( p.)ISSN: 0865- 2090.
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• 1999

  ČERMÁK, J. On the delay differential equation. Annales Polon.Math., 1999, vol. 71, no. 2, p. 161 ( p.)ISSN: 0066- 2216.
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  ČERMÁK, J. Asymptotic estimation for functional differential equations with several delays. ARCHIVUM MATHEMATICUM, 1999, vol. 35, no. 4, p. 337 ( p.)ISSN: 0044- 8753.
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• 1998

  ČERMÁK, J. The asymptotic bounds of solutions of linear delay systems. Journal of Mathematical Analysis and Application, 1998, vol. 225, no. 8, p. 373 ( p.)ISSN: 0022- 247X.
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  ČERMÁK, J. On the asymptotic behaviour of solutions of some functional- differential equations. Mathematica Slovaca, 1998, vol. 48, no. 2, p. 187 ( p.)ISSN: 0139- 9918.
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• 1995

  ČERMÁK, J. Note on simultaneous solutions of a system of Schroders equations. Mathematica Bohemica, 1995, vol. 95, no. 120, p. 225 ( p.)ISSN: 0862- 7959.
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  ČERMÁK, J. Continuous transformations of differential equations with delays. Georgian Mathematical Journal, 1995, vol. 95, no. 2, p. 1 ( p.)ISSN: 1072- 947X.
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• 1993

  ČERMÁK, J. On transformations of functional- differential equations. ARCHIVUM MATHEMATICUM, 1993, vol. 29, no. 3- 4, p. 227 ( p.)ISSN: 0044- 8753.
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