Milan Tvrdý - Publications

• Monographs
• Journals
• Proceedings of International Conferences
• Proceedings of Regional Conferences
• Lecture Notes
• Research Reports
• Various
• Preprints
• Videos

• Monteiro Antunes G., Slavík A., Tvrdý M.
  

  Kurzweil-Stieltjes integral. Theory and Applications.
  World Scientific, Series in Real Analysis-Vol.15, November 2018, 400pp.  [ISBN: 978-981-4641-77-7 (hardcover),  ISBN: 978-981-4641-79-1 (ebook)]
  

• Tvrdý M.

  Stieltjesův integrál. Kurzweilova teorie (in Czech).
  Univerzita Palackého v Olomouci, Olomouc, 2012
  
  [PDF of updated version prepared in the frames of the MATAP Project, last update March 14, 2016]

• Rachůnková I., Staněk S., Tvrdý M.

  Solvability of Nonlinear Singular Problems for Ordinary Differential Equations.
  Hindawi, Book Series: Contemporary Mathematics and Its Applications Series Volume: 5   [ISBN: 9789774540400 (Paperback),  ISBN: 9789774540967 (PDF),   DOI: 10.1155/9789774540400]
   

• Rachůnková I., Staněk S., Tvrdý M.

  Singularities and Laplacians in Boundary Value Problems for Nonlinear Ordinary Differential Equations.
  In: Handbook of Differential Equations (Ordinary Differential Equations) Vol.3]  pp. 605-721.
  
  [PREPRINT]

• Tvrdý M.

  Differential and Integral Equations in the Space of Regulated Functions.
  Mem.Differential Equations Math. Phys.  25 (2002), 1-104.  [PREPRINT]

• Schwabik S., Tvrdý M., Vejvoda O.
  

  Differential and Integral Equations: Boundary Value Problems and Adjoints.   Academia and D.Reidel, Praha, 1979.  
  
  [PDF]

• Márquez Albés I., Slavík A., Tvrdý M.

  Duality for Stieltjes differential and integral equations.  Journal of Mathematical Analysis And Application, 519 (1) (2023), 126789;   (PREPRINT).

• Minhós F., Tvrdý M., Zima M.

  On the solvability of some discontinuous functional impulsive problems  Electron. J. Qual. Theory Differ. Equ. 2020, No. 91, 1-17.  on-line.

• Hanung U.M., Tvrdý M.

  On the relationsships between Stieltjes type integrals of Young, Dushnik and Kurzweil.  Mathematica Bohemica 144 (2019) (4), 357-372;  on-line.

• Cid J.Á., Infante G., Tvrdý M., Zima M.

  New results for the Liebau phenomenon via fixed point index.  Nonlinear Analysis - Real World Applications 35 (2017), 457–469;  on-line  (PREPRINT)

• Monteiro G.A., Hanung U.M., Tvrdý M.

  Bounded convergence theorem for abstract Kurzweil-Stieltjes integral.  Monatshefte für Mathematik 180 (2016), 409–434; DOI 10.1007/s00605-015-0774-z.  (See PREPRINT)

• Cid J.Á., Infante G., Tvrdý M., Zima M.

  A topological approach to periodic oscillations related to the Liebau phenomenon.  Journal of Mathematical Analysis and Applications 423 (2015), 1546-1556; DOI: 10.1016/j.jmaa.2014.10.054.  (See PREPRINT)

• Monteiro G.A., Tvrdý M.

  Continuous dependence of solutions of abstract generalized linear differential equations with potential converging uniformly with a weight.   Boundary Value Problems 2014 (71), 2014, 1-18.   (PDF)

• Cid J.A., Propst G., Tvrdý M.

  On the pumping effect in a pipe/tank flow configuration with friction.  Physica D: Nonlinear Phenomena   (2014) pp. 28-33; doi:10.3934/dcds.2013.33.283  (See PREPRINT)

• Monteiro G., Tvrdý M.

  Generalized linear differential equations in a Banach space: Continuous dependence on a parameter.  Discrete Contin. Dyn. Syst. 33 (1) (2013), 283-303,   doi:10.3934/dcds.2013.33.283  (See PREPRINT)

• Monteiro G., Tvrdý M.

  On Kurzweil-Stieltjes integral in a Banach space Mathematica Bohemica 137 (2012), 365-381.   (See PREPRINT)

• Halas Z., Monteiro G., Tvrdý M.

  Emphatic convergence and sequential solutions of generalized linear differential equations.  Mem.Differential Equations Math. Phys. 54 (2011), 27-49.  (See PREPRINT)

• Becvár J.,Doslá Z., Kurzweil J., Mawhin J., Medková D., Tvrdý M.

  Remembering Stefan Schwabik (1941-2009).  Mathematica Bohemica 136 (2011), 113-134.  (PDF.)

• Cabada A., Cid J.A., Tvrdý M.

  A generalized anti-maximum principle for the periodic one dimensional $p$-Laplacian with sign changing potential. Nonlinear Analysis T.M.A. 72 (2010), 3436-3446.   (See PREPRINT.)

• Halas Z., Tvrdý M.

  Continuous dependence of solutions of generalized linear differential equations on a parameter.  Funct. Differ. Equ. 16 (2009), No. 2, 299-313.(PDF.)

• Halas Z., Tvrdý M.

  Singular Periodic Impulse Problems.  Nonlinear Oscillations 11 (2008), No.1, 32-44. (See PREPRINT.)

• Cabada A., Lomtatidze A., Tvrdý M.

  Periodic problem with quasilinear differential operator and weak singularity.  Advanced Nonlinear Studies 7 (2007), 629-649.  (See PREPRINT.)

• Rachůnková I., Tvrdý M.

  Periodic singular problem with quasilinear differential operator,  Mathematica Bohemica  131 (2006), 321-336.  [PDF] 

• Rachůnková I., Tvrdý M.

  Second order periodic problem with phi-Laplacian and impulses.  Nonlinear Analysis, T.M.A. 63 (2005), e257-e266.  (See PREPRINT.)

• Rachůnková I., Tvrdý M.

  Periodic problems with phi-Laplacian involving non-ordered lower and upper functions.  Fixed Point Theory  6 (2005), 99-112.  (See PREPRINT.)

• Rachůnková I., Tvrdý M.

  Existence results for impulsive second order periodic problems.  Nonlinear Analysis, T.M.A. 59 (2004), 133-146.  (See PREPRINT.)

• Rachůnková I., Tvrdý M.

  Non-Ordered Lower and Upper Functions in Second Order Impulsive Periodic problems.  Dynamics of Continuous, Discrete and Impulsive Systems, Ser. A Math. Anal. 12 (2005), no. 3-4, 397-415.  (See PREPRINT.)

• Rachůnková I., Tvrdý M.

  Construction of non-constant lower and upper functions for impulsive periodic problems.   Electronic Journal of Qualitative Theory of Differential Equations,  (Proceedings of the 7'th Colloquium on the Qualitative Theory of Differential Equations, Szeged, Hungary) No.19 (2004) 1-8.  [PDF]

• Rachůnková I., Tvrdý M.

  Nonmonotone impulse effects in second-order periodic boundary value problems.  Abstract and Applied Analysis 2004:7 (2004), 577-590.   (See PREPRINT.)

• Rachůnková I., Tvrdý M, Vrkoč I.

  Resonance and multiplicity in periodic booundary value problems with singularity.  Mathematica Bohemica  128 (2003), 45-70.   [PDF]

• Rachůnková I., Tvrdý M.

  Impulsive Periodic Boundary Value Problem and Topological Degree.  Functional Differential Equations, Israel Seminar  9 (2002), No.3-4, 471-498.   (See PREPRINT.)

• Rachůnková I., Tvrdý M.

  Localization of nonsmooth lower and upper functions for periodic boundary value problems.  Mathematica Bohemica  127 (2002), 531-545.  [PDF]

• Rachůnková I., Tvrdý M., Vrkoč I.

  Existence of nonnegative and nonpositive solutions for second order periodic boundary value problems.  Journal of Differential Equations  176 (2001), 445-469.   (See PREPRINT.)

• Rachůnková I., Tvrdý M.

  Construction of lower and upper functions and their application to regular and singular periodic boundary value problems.  Nonlinear Analysis TMA, 47 (2001), 3937-3948.   (See PREPRINT.)

• Rachůnková I., Tvrdý M.

  Nonlinear systems of differential inequalities and solvability of certain nonlinear second order boundary value problems.  Journal of Inequalities and Applications 6 (2001), 199-226.   (See PREPRINT.)

• Rachůnková I., Tvrdý M.

  Method of lower and upper functions and the existence of solutions to singular periodic problems for second order nonlinear differential equations.  Mathematical Notes Miskolc 1 (2000), 135-143.   (See PREPRINT.)

• Tvrdý M.

  Linear boundary value problems for generalized differential equations.  Annales Mathematicae Silesiane 14 (2000), 51-80.  [PDF]

• Ligęza J., Tvrdý M.

  On systems of linear algebraic equations in the Colombeau algebra.  Mathematica Bohemica  124(1999), 1-14.  [PDF] 

• Tvrdý M.

  On the continuous dependence on a parameter of solutions of initial value problems for linear generalized differential equations.  Functional Differential Equations, Israel Seminar 5(1999), 483-498. (with new appendix from 2010)
  [PDF]

• Tvrdý M.

  Linear integral equations in the space of regulated functions.  Mathematica Bohemica  123 (1998), 177-212.  [PDF]

• Tvrdý M.

  Linear integral equations in the space of regulated functions.  Mem. Differential Equations Math. Phys.  12 (1997), 210-218.  [PDF]

• Tvrdý M.

  Linear bounded functionals on the space of regular regulated functions.  Tatra Mountains Mathematical Publications  8 (1996), 203-210.  [PDF]

• Tvrdý M.

  Linear distributional differential equations of the second order.  Mathematica Bohemica 119 (1994), 415-436.  [PDF]

• Pelant M., Tvrdý M.

  Linear distributional differential equations in the space of regulated functions.  Mathematica Bohemica 118 (1993), 379-400.  [PDF]

• Tvrdý M.

  Generalized differential equations in the space of regulated functions (Boundary value problems and controllability).  Mathematica Bohemica  116 (1991), 225-244.  [PDF]

• Tvrdý M.

  Regulated functions and the Perron-Stieltjes integral.  Casopis pro pestování matematiky  114 (1989), 187-209.  [PDF]

• Brown R. C., Tvrdý M., Vejvoda O.

  Duality theory for linear n-th order integro-differential operators with domain in L^p determined by interface side conditions.  Czechoslovak Mathematical Journal 32 (107) (1982), 183-196. [PDF]

• Brown R. C., Tvrdý M.

  Generalized boundary value problems with abstract side conditions and their adjoints II.  Czechoslovak Mathematical Journal 31 (106) (1981), 501-509. [PDF]

• Brown R. C., Tvrdý M.

  Generalized boundary value problems with abstract side conditions and their adjoints I.  Czechoslovak Mathematical Journal 30 (105) (1980), 7-27. [PDF]

• Schwabik S., Tvrdý M.

  Boundary value problems for generalized linear differential equations.  Czechoslovak Mathematical Journal 29 (104) (1979), 451-477. [PDF]

• Tvrdý M.

  Fredholm-Stieltjes integral equations with linear constraints: duality theory and Green's function.  Casopis pro pestování matematiky 104 (1979), 357-369. [PDF]

• Tvrdý M.

  Note on functional-differential equations with initial functions of bounded variation.  Czechoslovak Mathematical Journal 25 (100) (1975), 67-70. [PDF]

• Tvrdý M.

  Linear boundary value type problems for functional-differential equations and their adjoints.  Czechoslovak Mathematical Journal 25 (100) (1975), 37-66. [PDF]

• Tvrdý M.

  Boundary value problems for generalized linear integrodifferential equations with left-continuous solutions.   Casopis pro pestování matematiky 99 (1974), 147-157. [PDF]

• Tvrdý M.

  Boundary value problems for linear generalized differential equations and their adjoints.  Czechoslovak Mathematical Journal 23 (98) (1973), 183-217. [PDF]

• Schwabik S., Tvrdý M.

  On the generalized linear ordinary differential equation.  Casopis pro pestování matematiky 98 (1973), 206-211. [PDF]

• Tvrdý M., Vejvoda O.

  General boundary value problem for an integrodifferential system and its adjoint II.  Casopis pro pestování matematiky 98 (1973), 26-42. [PDF]

• Tvrdý M., Vejvoda O.

  General boundary value problem for an integrodifferential system and its adjoint I.  Casopis pro pestování matematiky  97 (1972), 399-419. [PDF]

• Vejvoda O., Tvrdý M.

  Existence of solutions to a linear integro-boundary-differential equation with additional conditions.  Annali di Matematica Pura ed Applicata 9 (1971), 169-216.

• Tvrdý M.

  The normal form and the stability of solutions of a system of differential equations in the complex domain.  Czechoslovak Mathematical Journal 20 (95) (1970), 39-73. [PDF] and Correction [PDF]

• Mesquita Macena M.C.S., Tvrdý M.

  On the Existence of Bifurcation Points for Periodic Problems to Distributional Differential Equations. QUALITDE 2023, Razmadze Institute, Tbilisi, Georgia. (PREPRINT).

• Tvrdý M.

  Duality for Stieltjes Integral Equations.  International Workshop QUALITDE–2022, December 17–19,2022 (Tbilisi, Georgia), pp. 222-227. [PDF]

• Rachůnková I., Tvrdý M.

  Method of lower and upper functions in impulsive periodic boundary value problems.  Proceedings of EQUADIFF 2003 (Hasselt, Belgium), 252-257, World Sci. Publ., Hackensack, NJ, 2005   [PDF]

• Tvrdý M.

  Differential and integral equations with regulated solutions.  Proceedings of the "Conference EQUAM" (Varenna 1992, May 25-29), SAACM 3 (1993), 291-304.  [PDF]

• Tvrdý M.

  On optimal control of systems with interface side conditions.  Equadiff 6  (Proceedings, Brno, August 26-30, 1985),   ed. by J. Vosmanský and M. Zlámal),  J.E.Purkyne University, Dept.of Mathematics, Brno and Springer-Verlag, Berlin-Heidelberg-New York,  1986, 187-190. [PDF]

• Tvrdý M., Vejvoda O.

  Periodic solutions of weakly perturbed autonomous functional-differential equations.  Qualitative Methods of the Theory of Nonlinear Oscillations  (Proceedings, Kiev, August 30-September 6, 1981,  ed. by Yu. A. Mitropolsky),  Naukova dumka, Kiev,  1984, 375-379.

• Tvrdý M.

  On the controllability of linear Fredholm-Stieltjes integral operator.  Functional-Differential Systems and related topics III  (Proceedings, Blazejewko, May 22-29, 1983,  ed.by Michal Kisielewicz),  The Higher College of Engineering in Zielona Gora, 1983, 247-252.

• Brown R. C., Tvrdý M., Vejvoda O.

  On the operator theory of interface boundary value problems.  Functional-Differential Systems and related topics II   (Proceedings, Blazejewko, May 3-10, 1981,  ed. by Michal Kisielewicz),  The Higher College of Engineering in Zielona Gora, 1981, 40-46.

• Schwabik S., Tvrdý M.

  On linear problems in the space BV.  Equadiff IV  (Proceedings, Prague, August 22-26, 1977, ed. by Jirí Fabera),  Lecture Notes in Mathematics, Springer-Verlag, Berlin-Heidelberg-New York,  1979, 366-373. [PDF]

• Tvrdý M.

  Linear functional-differential operators: normal solvability and adjoints.  Colloquia Mathematica Societatis Janos Bolyai 15 (1975), 379-389.

• Tvrdý M.

  Boundary value problems for ordinary differential equations (in Czech).  Matematické metody řešení fyzikálních problémů  (Proceedings, Cikháj, 27 - 31. 05. 1985, ed. J. Nadrchal),  Universita J. E. Purkyne, Katedra matematiky, Brno, 1986, 92-106.

• Tvrdý M.

  Linear integral equations (in Czech).  CSVTS, Praha, 1974, 60 pp.

• Benes V., Kopáčková M., Tvrdý M.

  Mathematical solution of the transport equation for determining longitudinal hydrodynamic dispersivity using the single well tracer pulse method.  Research report, Stavební geologie Praha, 1985, 84 pp.

• Jarník J., Schwabik S., Tvrdý M., Vrkoč I.

  Jaroslav Kurzweil šedesátníkem (in Czech).   Casopis pro pestování matematiky 111 (1986), 91-111.

• Jarník J., Schwabik S., Tvrdý M., Vrkoč I.

  Sixty years of Jaroslav Kurzweil.  Czechoslovak Mathematical Journal 36 (111) (1986), 147-166.

• Mesquita Macena M.C.S., Tvrdý M.

  Bifurcation of periodic solutions to nonlinear measure differential equations.  (PREPRINT).

• Cid J.Á., Infante G., Tvrdý M., Zima M.

  New results for the Liebau phenomenon via fixed point index.   [ arXiv:1606.03602 [math.CA]]  (Final published in  Nonlinear Analysis - Real World Applications   35 (2017), 457–469;  (PREPRINT))

• Monteiro G., Hanung U.M., Tvrdý M.

  Bounded convergence theorem for abstract Kurzweil-Stieltjes integral.  [ arXiv:1412.0993 [math.CA]]  (Final version published in  Monatshefte für Mathematik 180 (2016), 409–434; DOI 10.1007/s00605-015-0774-z, doi: 10.1007/s00605-015-0774-z.)

• Cid J.Á., Infante G., Tvrdý M., Zima M.

  A topological approach to periodic oscillations related to the Liebau phenomenon.  [ arXiv:1408.0130 [math.CA]]  (Final version published in  Journal of Mathematical Analysis and Applications 423 (2015), 1546-1556; doi: 10.1016/j.jmaa.2014.10.054.)

• Monteiro G., Tvrdý M.

  Continuous dependence of solutions of abstract generalized linear differential equations with potential converging uniformly with a weight.  [PDF]  (Final version published in   Boundary Value Problems 2014 (71), 2014, 1-18.)

• Cid J.A., Propst G., Tvrdý M.

  On the pumping effect in a pipe/tank flow configuration with friction.  [PDF]  (Final version published in  Physica D: Nonlinear Phenomena  (2014) 28-33; doi:10.3934/dcds.2013.33.283.)

• Halas Z., Monteiro G., Tvrdý M.

  Emphatic convergence and sequential solutions of generalized linear differential equations.  [PDF] (Final version published in  Mem. Differential Equations Math. Phys. 54 (2011), 27-49.)

• Monteiro G., Tvrdý M.

  Generalized linear differential equations in a Banach space: Continuous dependence on a parameter.  [PDF] (Final version published in   Discrete Contin. Dyn. Syst. 33 (1) (2013), 283-303,   doi:10.3934/dcds.2013.33.283)

• Monteiro G., Tvrdý M.

  On Kurzweil-Stieltjes integral in a Banach space.  [PDF] (Final version published in  Mathematica Bohemica. 137 (2012), 365-381.)

• Cabada A., Cid J.A., Tvrdý M.

  A generalized anti-maximum principle for the periodic one dimensional $p$-Laplacian with sign changing potential.  [PDF] (Final version published in  Nonlinear Analysis T.M.A. 72 (2010), 3436-3446.)

• Halas Z., Tvrdý M.

  Approximated Solutions of Generalized Linear Differential Equations.  Mathematical Institute, Academy of Sciences of the Czech Republic, Preprint 141 (2008)   [PDF]  [PDF [updated version August 2009]] (Part of the final version published in  Funct. Differ. Equ. 16 (2009), No. 2, 299-313. )

• Halas Z., Tvrdý M.

  Singular Periodic Impulse Problems.  Mathematical Institute, Academy of Sciences of the Czech Republic, Preprint 171 (2007)   [PDF].) (Final version published in  Nonlinear Oscillations 11 (2008), No.1, 32-44. )

• Cabada A., Lomtatidze A., Tvrdý M.

  Periodic problem with quasilinear differential operator and weak singularity.  Mathematical Institute, Academy of Sciences of the Czech Republic, Preprint 167 (2006)  [corrected and extended version from April 2, 2007].   [PDF] (Final version published in  Advanced Nonlinear Studies 7 (2007), 4, 629-649. )

• Rachůnková I., Stanek S., Tvrdý M.

  Singularities and Laplacians in Boundary Value Problems for Nonlinear Ordinary Differential Equations.  Preliminary version of a chapter submitted for Handbook of Differential Equations Ordinary Differential Equations) Vol.3]  [PDF]

• Rachůnková I., Tvrdý M.

  Second order periodic problem with phi-Laplacian and impulses.  Faculty of Science, Palacký University, Preprint 14/2004.  [PDF] (Final version published in   Nonlinear Analysis, T.M.A.. )

• Rachůnková I., Tvrdý M.

  Periodic problems with phi-Laplacian involving non-ordered lower and upper functions.  Faculty of Science, Palacký University, Preprint  2004.  [PDF] (Final version published in   Fixed Point Theory  6 (2005), 99-112.)

• Rachůnková I., Tvrdý M.

  Second Order Periodic Problem with phi-Laplacian and Impulses - Part II.  Mathematical Institute, Academy of Sciences of the Czech Republic, Preprint 156 (2004).  [PDF]

• Rachůnková I., Tvrdý M.

  Second Order Periodic Problem with phi-Laplacian and Impulses - Part I.  Mathematical Institute, Academy of Sciences of the Czech Republic, Preprint 155 (2004).  [PDF]

• Rachůnková I., Tvrdý M.

  Periodic Boundary Value Problems for Nonlinear Second Order Differential Equations with Impulses - Part III.  Mathematical Institute, Academy of Sciences of the Czech Republic, Preprint 153 (2003).  [PDF]
  (Final version entitled "Existence Results for Impulsive Second Order Periodic Problems" published in Nonlinear Analysis, T.M.A. 59 (2004), 133-146.)

• Rachůnková I., Tvrdý M.

  Periodic Boundary Value Problems for Nonlinear Second Order Differential Equations with Impulses - Part II.  Mathematical Institute, Academy of Sciences of the Czech Republic, Preprint 151 (2002).  [PDF]
  (Final version entitled "Non-ordered Lower and Upper Functions in Second Order Impulsive Periodic Problems" accepted to Dynamics of Continuous, Discrete and Impulsive Systems.)

• Rachůnková I., Tvrdý M.

  Periodic Boundary Value Problems for Nonlinear Second Order Differential Equations with Impulses - Part I.  Mathematical Institute, Academy of Sciences of the Czech Republic, Preprint 148 (2002).  [PDF]
  (Final version entitled "Nonmonotone impulse effects in second-order periodic boundary value problems" published in   Abstract and Applied Analysis 2004:7, 577-590.) 

• Rachůnková I., Tvrdý M.

  Impulsive Periodic Boundary Value Problem and Topological Degree.  Faculty of Science, Palacký University, Preprint 9/2002.  [PDF]
  (Final version published in Functional Differential Equations, Israel Seminar  9 (2002), No.3-4, 471-498.)

• Rachůnková I., Tvrdý M.

  Construction of lower and upper functions and their application to regular and singular periodic boundary value problems.  Faculty of Science, Palacký University, Preprint 19/2000.  [PDF]
  (Final version published in Nonlinear Analysis, T.M.A. 47 (2001), 3937-3948.)

• Rachůnková I., Tvrdý M.

  On the construction of nonconstant lower and upper functions to second order nonlinear periodic boundary value problems.  Mathematical Institute, Academy of Sciences of the Czech Republic, Preprint   135 (2000).  [PDF]

• Rachůnková I., Tvrdý M.

  Method of lower and upper functions and the existence of solutions to singular periodic problems for second order nonlinear differential equations.  [PDF] (Final version published in Mathematical Notes Miskolc  1(2000),135-143.)

• Rachůnková I., Tvrdý M., Vrkoč I.

  Existence of nonnegative and nonpositive solutions for second order periodic boundary value problems.  Mathematical Institute, Academy of Sciences of the Czech Republic, Preprint 134 (1999).  [PDF]
  (Final version published in   Journal of Differential Equations  176 (2001), 445-469.)

• Rachůnková I., Tvrdý M.

  Nonsmooth lower and upper functions and solvability of certain nonlinear second order BVP's,  Faculty of Science, Palacký University, Preprint  5/1999.  [PDF]
  (Final version entitled "Nonlinear systems of differential inequalities and solvability of certain nonlinear second order boundary value problems" published in   Journal of Inequalities and Applications 6  (2001),199-226.)

Videos

• Tvrdý M.
  

  Kurzweil-Stieltjes integral (Introduction to the modern theory of Stieltjes integration).  [video]
  51 Congreso Nacional de la Sociedad Matemática Mexicana 2018. Universidad Juárez Autónoma de Tabasco (October 2018)
  

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