prof. RNDr. Milan Medveď, DrSc.

miestnosť (room): M 104
telefón (phone): (02/602 95) 103
e-mail: Milan.Medved@fmph.uniba.sk

Učenie (Teaching)
Oblasti záujmu a výskumu (Current research and areas of interest)
  • Dynamické systémy (Dynamical systems)
  • Teória bifurkácií (Bifurcation theory)
  • Integrálne nerovnosti (Integral inequalities)
  • Teória riadenia a diferenciálnych hier (Control theory and differential games)

Publikácie (Publications)
    Monografie (Monographs)
  • M. Medveď: Dynamical Systems , Veda, Bratislava 1988 (in Slovak) (Book Rewies: A. Klíč: Applications of Mahematics 1993, P. Brunovský: MR 90 k:58057)
  • M. Medveď: Fundamentals of Dynamical Systems and Bifurcation Theory, Adam Hilger, Bristol, New York, Philadelphia 1992, (Book Review: D. K. Arrowsmith, SIAM Review, Vol. 36, No. 1(1994), D. R. J. Chilingworth, Contemporary of Physics, Vol. 33, No. 5(1992), J. Scheurle,, Bulletin of the Amer. Math. Soc., Vol. 31, No. 1(1994) )

    • Učebnice (Text-books)
  • M. Medveď: Dynamical Systems, Comenius University, Bratislava 2000 (in Slovak)

    Vedecké články (Scientific papers)
  • M. Medveď: Remark on the properties of solutions of linear second order differential equations, AFRN, Comen. Math. XIX (1968), 191-195 (in Slovak)
  • M. Medveď: Sufficient conditions for the non-oscillation of nonhomogeneous linear n-th order differential equations, Matematický časopis 18(1969), 99-104
  • M. Medveď: generalizations of Bihari lemma and their applications, Matematický časopis 20(1970), 225-232 (in Slovak)
  • M. Medveď : Generic properties of parametrized vector fields I, Czechosl. Math. J. 25(1975), 376-388
  • M. Medveď: Generic properties of parametrized vector fields II, Czechosl. Math. J. 26(1976), 71-83
  • M. Medveď: On a problem of evasion, Kybernetika 13(1977), 57-62
  • M. Medveď: On a class of evasion games, Časopis pro pěst. matem. 102(1977), 9-24
  • M. Medveď: Generic bifurcations of second order ordinary differential equations on differentiable manifolds, Math. Slovaca 27(1977), 2-24
  • M. Medveď: On generic bifurcations of second order ordinary differential equations near closed orbits, Asterisque 50(1977), 23-29
  • M. Medveď: Generic properties of linear control systems depending on a parameter, Annales Polonici Math., XXXIV(1977), 23-29
  • M. Medveď: On a differential game of evasion described by a class of nonlinear integrodifferential equations, Czechosl. Math.J. 28(1978), 407-418
  • M. Medveď: On a differential game of evasion described by a class of nonlinear integrodifferential equations, Optimization Techniques, Proceedings of the 9 th IFIP Conference on Optimization Techniques, Warsaw 1979, Springer-Verlag 1980, 232-240
  • M. Medveď: Generic bifurcations of vector fields with a singularity of codimension 3, Proceedings of the 5 th Czechoslovak Conference on Differential Equations and their Applications, Equadiff 5, Teubner-Verlag 47, 1982, 260-263
  • M. Medveď: Generic bifurcations of second order ordinary differential equations near closed orbits, J. of Differential Equations, Vol. 37, No. 1 (1980), 98-107
  • M. Medveď: On a codimension three bifurcations of a family of three-dimensional vector fields, Equadiff 82, LNM 1017, Springer-Verlag 1983, 453-461
  • M. Medveď: On two-parametric systems of matrices and diffeomorphisms, Czechosl. Math. J. 33(1983), 176-192
  • M. Medveď: On genericity of complete controllability in the space of linear parametrized control systems, Math. J, 2(1983), 167-175
  • M. Medveď: Vector fields with a codimension three singularity and their parametric defoemation, Proceeding of the 9 th Conference on Nonlinear Oscillations, Vol. 2, Kiev 2, 1981, Naukova Dumka 1984 (in Russian)
  • M. Medveď: On a codimension three bifurcation, Časopis pro pěst. matem. 109(1984), 3- 26
  • M. Medveď: The unfolding of a germ of vector fields in the plane with a singularity of imension 3, Czechosl. Math. J. 35(1985), 1-42
  • M. Medveď: Normal forms and bifurcations of some equivariant vector fields, Math. Slovaca 23(1987), 19-31
  • M. Medveď: Almost Floquet linear difference equations, Math. Slovaca 37(1987), 367-373
  • M. Medveď: On a nonlinear differential game of evasion with constraints, Kybernetika 1, 23(1987), 19-31
  • M. Medveď: Dynamical systems and evolutionary proceses, Filozofia 44(1989), 7-21 (in Slovak)
  • M. Medveď: On two-sided solutions of linear integrodifferential equations of Volterra type with infinite delay, Časopis pro pěst. matem. 115(1990), 164-172
  • M. Medveď: On a codimension three bifurcation of plane vector fields with Z2 symmetry Czechosl. Math. J., 40(115)(1990), 295-310
  • M. Medveď: On minimal periods of functional-differential equations and difference inclusions, Annales Polonici Math., LIV.3 (1991), 263-270
  • M. Medveď: Normal forms of implicit and observed implicit differential equations, Rivista di Mathematica Pura ed Appl. 10(1992), 97-107
  • M. Medveď: Bihari type inequalities with multiple integral and delay, Periodica Mathematica Hungarica, Vol. 27, No. 3 (1993), 207-212
  • M. Medveď: Qualitative properties of generalized vector fields, Rivista di Mathematica Pura ed Appl. 15(1994), 7-31
  • M. Medveď: Special solutions of linear difference equations with infinite delay, Archivum Math. (Brno), 30(1994), 127-149
  • M. Medveď: A class of vector fields on maniforls containing second order ODEs, Hiroshima Math. J. 26(1996), 127-149
  • M. Medveď: A new approach to an analysis of Henry type integral inequalities and their Bihari type versions, J. Math. Anal. Appl. 214(1997), 349-366
  • M. Medveď: Singular integral inequalities and stability of semilinear parabolic equations, Archivum Math. (Brno), 34(1998), 179-186
  • M. Medveď: Generic saddle-node bifurcation for cascade second order ODEs on manifolds, Annales Polonici Math., 68(1998), 176-186
  • M. Medveď: Nonlinear singular integral inequalities for functions in two and n independent variables, J. of Inequalities and Appl. 5(2000), 287-308
  • M. Medveď: Nonlinear singular difference inequalities suitable for discretizations of parabolic equations, Demonstratio Math., XXXIII, No. 3 (2000), 517-529
  • M. Medveď: Integral inequalities and global solutions of semilinear evolution equations, J. Math. Anal. Appl. 267(2002), 643-650
  • M. Medveď: On the existence of global solutions of evolution equations, Demonstratio Math., Vol. 37 , No. 4 (2004), 871-882
  • M. Medveď, E. Pekárková: Existence of global solutions for systems of second-order differential equations with p-Laplacian, Electronic Journal of Differential Equations, Vol. 2007, No. 136(2007), 1-9
  • M. Medveď: On the global existence of mild solutions of delay systems, FOLIA Facultatis Scientarium Naturalium Universitatis Masarykianae Brunensis, Mathematica 16, Colloquium on Differential and Difference Equations, CDDE 2006, Masaryk University (Brno 2007), pp.115-122
  • M. Medveď: On singular versions of Bihari and Wendroff-Pachpatte integral inequalities and their applications, Tatra Mountains Math. Publications, 39 (2007), 1-12
  • M. Medveď: Singular integral inequalities with several nonlinearities and integral equations with singular kernels, Nonlinear Oscillations, Vol. 11., No.1 (2008)
  • M. Bartušek, M. Medveď: Existence of global solutions for systems of second-order functional-differential equatiuons with p-Laplacian, Electronic Journal of Differential Equations, Vol. 2008, No. 40 (2008), 1-8
  • M. Medveď, E. Pekárková: Large tine behavior of solutions to second-order differential equations with p-Laplacian, Electronic J. of Differntial Equations , Vol. 2008 (2008), 1-12
  • M. Medveď: On the global existence if mild solutions of nonlinear delay systems associated with continuous and analytic semigroups, Electronic J. of Qualitative Theory of Differential Equations, Proc. 8th Coll.QTDE, 2008, No. 13, 1.10
  • M. Medveď, T. Moussaoui: Asymptotic integration of nonlinear $\Phi-$Laplacian differential equations, Nonlinear Analysis 72 (2010), 2000-2008
  • M. Medveď, M. Pospíšil, L. Škripková: Stability and the nonexistence of blowing-up solutions of nonlinear delay systems with linear parts defined by permutable matrices, Nonlinear Analysis (2011), doi.10.1016/j.na.2011.02.026.
  • M. Kirane, M. Medveď, N.A.Tatar: Semilinear Volterra integrodifferential problems with fractional derivatives in nonlinearities, Abstract and Applied Analysis, Article ID 510314, 2011.
  • J. Wang, Y. Zhou, M. Medveď:On the solvability and optimal controls of fractional integrodifferential evolution systems with infinite delay, Journal of Optimization Theory and Applications, Vol.125 (2012),31-50.
  • M. Kirane, M. Medveď, N.A.Tatar: On the nonexistence of blowing-up solutions to a fractional functional-differential equations, Georgia J.Math. 19 (2012), 127-144.
  • JinRong Wang, Yong Zhou, M. Medveď: Qualitative Analysis for Nonlinear Fractional Difeferntial Equations via Topological Degree Method, Topological Methods in Nonlinear Analysis, Vol. 40 (2012), 245-271 .
  • M. Medveď: On the asymptotic behavior of solutions of nonlinear differential equations of integer and also of non-integer order, Electronic J. of Qualitative Differential Equations, Proc. 9th.Coll.QTDE,2012,No.10,1-9.
  • JinRong Wang, Yong Zhou, M. Medveď: Picard and weakly Picard operator technique for nonlinear differential equations in Banach spaces, Journal of Math. Anal. Appl. , 389 (2012), 261-274.389 (2012),261-274.
  • M. Medveď, M. Pospíšil: Sufficient conditions for the asymptotic stability of nonlinear multidelay differential equations with linear parts defined by pairwise permutable matrices, Nonlinear Analysis, 75 (2012), 3348-3363.
  • M. Medveď, L. Škripková: Sufficient conditions for the exponential stability of delay difference equations with linear parts defined by permutable matrices, Electronic J.Qualitative Theory of Differential Equations, No.22 (2012), 1-13.
  • E. Brestovanská, M. Medveď: Fixed point theorems of the Banach and Krasnoseľskii type for mappings on m-tuple Cartesian product of Banach algebeas and systems of generalized Gripenberg's equations, Acta Univ. Palacki. Olomouc, Fac. Rer. Nat., Mathematica 51, 2 (2012), 27-39.
  • M. Medveď, M. Pospíšil: Representation and stability of solutions of systems of difference equations with multiple delays and linear parts defined by pairwise permutable matrices, Communications in Applied Analysis, 17, 1 (2013), 21-46.
  • M. Medveď: Asymptotic integration of some classes of fractional differential equations, Tatra Mountains Math. Publications Vol. 54 (2013), 1-14.
  • JinRong Wang, Yong Zhou M. Medveď: Existence and stability of fracational differential equations with Hadamard derivative, Topological Methods in Nonlinear Analysis, Vol. 41, No. 1 (2013), 113-133.
  • J. Wang, Y. Zhou, M. Medveď: Extremal solutions of Cauchy problems for abstract fractional differential equations, Math. Slovaca, Vol. 63 (2013), 769-792.
  • E. Brestovanská, M. Medveď: Solow differential equations on time scales – A unified approach to continuous and discrete Solow growth model, DEA-Differential Equations & Applications, Vol. 5, No. 4 (2013)
  • M. Medveď, M. Pospíšil, L. Škripková: On exponential stability of nonlinear fractional multidelay integrodifferential equations defined by pairwise permutable matrices, Applied Mathematics and Computations,227 (2014), 456-468.
  • E. Brestovanská, M. Medveď: Asymptotic behavior of solutions to second order differential equations with fractional derivative perturbations, Electronic J. of Differential Equations, Vol. 2014 (2014), No. 201, 1-10.
  • X. Li, M. Medveď, JinRongWang: Generalized boundary value problems for nonlinear fractional Langevin equations, Acta Univ. Palacki, Olomouc, Fac. Rer. Natur., Mathematica 53, 2 (2014), 85-100.
  • M. Medveď: Functional-differential equations with Rimemann-Liouville integrals in the nonlinearities, Mathematica Bohemica, 139, No. 4 (2014), 587-595.
  • M. Medveď: Exponential stability of solutions of nonlinear differential equations with Riemann-Liouville fractional integrals in the nonlinearities, Proceedings of 4 th Institute of Chemical Technology, Prague, Scientific Colloquium, June 24-26, 2014, 10-20.
  • A. A. Boichuk, M. Medveď, V. P. Zhuravliov: Fredholm boundary-value problems for linear delay systems defined by pairwise permutable matrices, EJQTDE, No. 23 (2015), 1-9.
  • M. Medveď, M. Pospíšil: Asymptotic integration of fractional differential equations wľith integrodifferential right-hand side, Mathematical Modelling and Analysis, Vol. 20, No. 4 (2015), 471-489.
  • E. Brestovanská, M. Medveď: Dynamical systems of a multi-capital growth model, Applied Mathematical Sciences, Vol. 9, No. 83 (2015), 5003-5008.
  • E. Brestovanská, M. Medveď: Solow multi-capital growth model described by a system of differential equations on time scales, Differential Equations and & Applications, Vol. 8, No. 3 (2016), 335-348.
  • M. Medveď, E. Pekárková: Asymptotic integration of differential equations with singular p-Laplacian, Archivum Mathematicum (Brno), Vol. 52 (2016), 13-19.
  • E. Brestovanská, M. Medveď: Exponential stability of solutions of a second order systém of integrodifferential equations with the Caputo-Fabrizio fractional derivatives, Progr. Fract. Differ. Appl., Vol. 2, No. 3 (2016), 187-192.
  • M. Medveď, M. Pospíšil: Representation of solutions of systems of linear differential equatios with multiple delays and linear parts given by nonpermutable matrices, Nonlinear Oscillations, Vol. 19, No. 4 (2016), 521-532.
  • E. Brestovanská, F. Jaroš, M. Medveď: Existence results for systems of iterative differential equations, Miskolc Mathematical Notes. - Vol. 18, No. 2 (2017), s. 655-664
  • E. Brestovanská, M. Medveď: Exponential stabiliy of solutions of nonlinear fractionally perturbed ordinary differential equations, Electronic J. of Differential Equations, Vol. 2017 (2017), No. 201, 1-17.
  • M. Medveď, M. Pospíšil: Representation of Solutions of Systems of Linear Differential Equations with Multiple Delays and Linear Parts Given by Nonpermutable Matrices, Journal of Mathematical Sciences. - Roč. 228, č. 3 (2018), s. 276-289
  • E. Brestovanská, M. Medveď: New conditions for the exponential stability of fractionally perturbed ODEs, Electronic Journal of Qualitative Theory of Differential Equations [elektronický dokument]. - Roč. 84 (2018), s. 1-14
  • E. Brestovanská, M. Medveď: Sufficient conditions for the exponential stability of nonlinear fractionally perturbed ODEs with multiple time delays, Fractional Differential Calculus. - Roč. 9, č. 2 (2019), s. 263-278
  • M. Medveď, M. Pospíšil: On the existence and exponential stability for differential equations with multiple constant delays and nonlinearity depending on fractional substantial integrals, Electronic Journal of Qualitative Theory of Differential Equations [elektronický dokument]. - č. 43 (2019), s. 1-17
  • E. Brestovanská, M. Medveď: Differential equations with tempered Psi-fractional derivative, Mathematical Modelling and Analysis. - Roč. 26, č. 4 (2021), s. 631-650
  • M. Medveď, M. Pospíšil: Stability and feedback stabilizability of delay periodic differential equations with pairwise permutable matrix functions, Mathematica Slovaca. - Roč. 72, č. 2 (2022), s. 379-396
  • M. Medveď, M. Pospíšil, E. Brestovanská: Nonlinear Integral Inequalities Involving Tempered Psi-Hilfer Fractional Integral and Fractional Equations with Tempered Psi-Caputo Fractional Derivative, Fractal and Fractional [elektronický dokument]. - Roč. 7, č. 8 (2023), s. 1-17, art. no. 611
  • M. Medveď, M. Pospíšil:Generalized Laplace Transform and Tempered Psi-Caputo Fractional Derivative, Mathematical Modelling and Analysis. - Roč. 28, č. 1 (2023), s. 146-162
  • M. Medveď: Normal Forms, Holomorphic Linearization and Generic Bifurcations of Dynamic Equations on Discrete Time Scales, Journal of Dynamics and Differential Equations : Special Issue in Memory of Pavol Brunovský. - Roč. 36, č. 1 (2024), s. 53-69

    Ostatné články (Other papers)
  • P. Brunovský, M. Medveď: Bifurcations of nongradient systems and catastrophe theory, Pokroky, matematiky, fyziky a informatiky, Vol. 37, No. 1 (1980), 97-107 (in Slovak)
  • M. Medveď: Reflextions on nontraditional applications of mathematics, Matematické obzory 9(1976), 73-91 (in Slovak)
  • M. Medveď: Some qualitative methods in contemporary mathemmatics, Proceedings of the Symposium on formalization of scientific research, Institute of Phylosophy and Sociology, Slovak Academy of Sciences, Bratislava 1986 (in Slovak)
  • M. Medveď: Catastrophes and then chaos only, Matematické obzory 26(1986), 7-21
  • M. Medveď: K životnému jubileu profesora Pavla Brunovského, Naša univerzita (Február 2005), č. 6

    • Book Rewies
  • M. I. Camacho, M. J. Pacifico, and F. Takens: Dynamical Systems and Bifurcation Theory, Pitman Research Notes in Mathematics, 160, Longman Group UK Limited, 1987, 421 pp. (M. Medveď, in Acta Applicandae Mathematicae 17 (1989))

    • Editor zborníkov (Editor of Proceedings)
  • Czech – Slovak Conference on Differential Equations and Their Applications, Equadiff 8, Tatra Mountains Mathematical Publications, Vol. 4, 1994 (Editors: Pavol Brunovský, Milan Medveď)
  • Czech – Slovak Conference on Differential Equations and Their Applications, Equadiff 11, Bratislava 2005 Procedings of minisymposia and contributed talks
  • On a nonlinear...., Equadiff 2007, Vienna, August 5-11, 2007

    • Abstrakty (Abstracts)
  • M. Medveď: Nonlinear integral inequalities with singular kernels and their applications, International Conference on Differential quations, Czecho-Slovak series, Equadiff 11, Comenius University, Bratislava, Slovakia, July 25-29, 2005, pp. 57
  • M. Medveď: On the global existence and stability of mild solutions of delay systems, Colloquium on Differential and Difference Equations, September 5-8, Brno 2006, Czech Republic, pp. 48
  • M. Medveď: On singular versions of the Bihari and Wendroff type integral inequalities and their applications, Conference on Differential and Difference Equations and Applications, Rajecké Teplice, June 26-30, 2006, pp. 34
  • M. Medveď: On the global existence of mild solutions of nonlinear delay systems associated with continuous and analytic semigroups, Eight Colloquium on the Qualitative Theory of Differential Equations, Szeged 2007, June 25-28, Szeged, Hungary
  • M. Medveď: On a nonlinear integral inequality and its applications to the study of global properties of differential equations with delay, Equadiff 2007 , August 5-11, 2007, Vienna, pp-93-94
  • M. Medveď: On a nonlinear version of the Henry integral inequality, Equadiff 12, July 20-24, Brno 2009, pp. 105
  • M. Medveď: On the asymptotic behavior of solutions of nonlinear differential equations of integer and also non-integer orders, 8th Colloquium on the Qualitative Theory of Differential Equations, Szeged, June 28-July 1, 2011, Szeged, Hungary, 35-35.
  • M. Medveď: Asymptotic integration of some classes of fractional differential equations, Conference on Differential and Difference Equations and Applications, Terchová, June 25-29, 2012.
  • M. Medveď: On exponential stability of fractionally perturbed ODEs,Veszprém Conference on Differential and Difference Equations and Applications : Abstracts [elektronický dokument]. - : 1. vyd. Vesprém : Pannon Egyetem, 2018. - S. 25-25

    • Research Projects
  • VEGA project No. 1/0507/11 Kvalitatívne vlastnosti diferenciálnych rovníc celočíselného a neceločíselného rádu (Qualitative properties of differential equations of integer and noninteger order) (principal investigator)
  • APVV project No. APVV-0414-07 Nelineárne javy v evolučných rovniciach (Nonlinear phenomena in evolution equations) (pricipal investigator: prof. Marek Fila)
  • VEGA project No. 1/0071/14 Kvalitatívne vlastnosti diferenciálnych rovníc celočíselného a neceločíselného rádu (Qualitative properties of differential equations of integer and noninteger order) (principal investigator)

    • Editorial Boards
  • Applications of Mathematics, Institute of Mathematics, Academy of Sciences, Prague, Czech Republic
  • Acta Universitatis, Palackianae Olomucensis, Facultas Rerum Naturalium, MATHEMATICA, Faculty of Science, Palacky University, Olomouc, Czech Republic
  • Acta Mathematica, Universitatis Comenianae, Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia