Research
- Qualitative theory of partial and ordinary differential equations, oscillation properties.
- Qualitative theory of linear and half-linear difference equations.
- Application of mathematics to selected problems in biology, forestry, urban forestry, material engineering
- Researcher ID page
- ORCID 0000-0001-7109-1526
- Scopus Author ID 6602164820.
- My profile in university information system and Google Scholar
Published research papers
- V. Cristini, J. Tippner, M. Tomšovský, J. Zlámal, R. Mařík, Acoustic tomography outputs in comparison to the properties of degraded wood in beech trees. European journal of wood and wood products. 2022. sv. 80, č. 6, s. 1377–1387. ISSN 0018-3768. URL: https://doi.org/10.1007/s00107-022-01872-w
- B. Vojáčková, J. Tippner, P. Horáček, V. Sebera, L. Praus, R. Mařík, M. Brabec, The effect of stem and root-plate defects on the tree response during static loading - Numerical analysis, Urban Forestry & Urban Greening Volume 59, April 2021. online
- S. Fišnarová, R. Mařík, Oscillation of second order half-linear neutral differential equations with weaker restrictions on shifted arguments, Mathematica Slovaca, vol. 70 (2020) No.2, 389-400. ISSN 0139-9918. IF.
- S. Fišnarová, R. Mařík, Oscillation of neutral second order half-linear differential equations without commutativity in deviating arguments, Mathematica Slovaca, vol. 67 No. 3 (2017), 701–718. ISSN 0139-9918. online, IF=0.346
- R. Mařík, On the influence of delay to the strength of oscillation criteria for neutral second order half-linear differential equations, RIMS Kôkyûroku series No. 1959 (2015), 1-14. online
- S. Fišnarová, R. Mařík, Modified Riccati technique for half-linear differential equations with delay, Electron. J. Qual. Theory Differ. Equ. 2014, No. 64, 1-14. online, PDF, IF=0.638
- R. Mařík, Remarks on the paper by Sun and Meng, Appl. Math. Comput. 174 (2006), Appl. Math. Comput 248 (2014), 309–313. ISSN 0096-3003. online, PDF, doi: 10.1016/j.amc.2014.09.100, IF=1.60
- P. Hasil, R. Mařík, M. Veselý, Conditional oscillation of half-linear differential equations with coefficients having mean values, Abstr. Appl. Anal. Volume 2014 (2014), Article ID 258159, 14 pages. online, PDF, IF=1.102
- S. Fišnarová, R. Mařík, On eventually positive solutions of quasilinear second order neutral differential equations, Abstr. Appl. Anal. Volume 2014 (2014), Article ID 818732, 11 pages. online, PDF, IF=1.102
- S. Fišnarová, R. Mařík, Oscillation criteria for neutral second-order half-linear differential equations with applications to Euler type equations, Bound. Value Probl. 2014:83 (2014), 1-14. online, PDF,IF=0.92
- S. Fišnarová, R. Mařík, Oscillation of half-linear differential equations with delay, Abstr. Appl. Anal. Volume 2013 (2013), Article ID 583147, 6 pages. online, PDF, IF=1.102
- O. Došlý, S. Fišnarová, R. Mařík, Power comparison theorems in half-linear oscillation theory, J. Math. Anal. Appl. (2013) vol. 401, No. 2, pp. 611-619. ISSN 0022-247X. online, doi: 10.1016/j.jmaa.2012.12.029, PDF, IF=1.001
- S. Fišnarová, R. Mařík, Local estimates for modified Riccati equation in theory of half-linear differential equation, Electron. J. Qual. Theory Differ. Equ. 2012, No. 63, 1-15. online, MathScinet, PDF, IF=0.74
- R. Mařík, Coupled intervals for discrete p-degree functional, Adv. Difference Equ., 2012:100. doi: 10.1186/1687-1847-2012-100, online, PDF, IF=0.85
- R. Mařík, Summation comparison theorems for half-linear second order difference equations on finite interval, Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis (2011) 59, No. 7, pp 245-248. ISSN 1211-8516. online, PDF
- S. Fišnarová, R. Mařík, On Constants in Nonoscillation Criteria for Half-Linear
Differential Equations, Abstr. Appl. Anal. 2011. (2011),
č. 638271, s. 1-15. ISSN 1085-3375.
online, doi: 10.1155/2011/638271, PDF, IF=1.442 - S. Fišnarová, R. Mařík, Half-linear ODE and modified Riccati equation: Comparison theorems, integral characterization of principal solution, Nonlinear Anal., vol. 74 (2011), issue 17, pages 6427-6433. online, PDF, IF=1.279
- O. Došlý, S. Fišnarová, R. Mařík, Comparison theorems for Riccati inequalities arising in the theory of PDE’s with p-Laplacian, Electron. J. Differential Equations, No. 53. (2011), 1-9. online, PDF
- R. Mařík, A remark on connection between conjugacy of half-linear differential equation and equation with mixed nonlinearities, Appl. Math. Lett. 24 (2011), 93-96. online, doi: 10.1016/j.aml.2010.08.024, PDF, IF=0.978
- S. Fišnarová, R. Mařík, Generalized Picone and Riccati inequalities for half-linear differential operators with arbitrary elliptic matrices, Electron. J. Differential Equations 2010. vol. 2010, 111, p. 1-13. ISSN 1072-6691. online, PDF
- R. Mařík, Conjugacy criteria for half-linear ODE in theory of PDE with generalized p-Laplacian and mixed powers, Nonlinear Anal. Vol. 73 (2010), No. 2, 500-509. online, doi: 10.1016/j.na.2010.03.045, IF=1.487
- R. Mařík, Ordinary differential equations in the oscillation theory of partial half-linear differential equation, J. Math. Anal. Appl. 2008. sv. 338, č. 338, s. 194-208. online, doi: 10.1016/j.jmaa.2007.05.015, IF=1.046 (2008)
- L. Baráková, R. Mařík, An age-structured model of cannibalism, Electron. J. Differential Equations, Vol. 2006(2006), No. 106, 1-11. online, PDF
- R. Mařík, Interval-type oscillation criteria for half-linear PDE with damping, Appl. Appl. Math., Vol. 1 (2006), No 1, 1-10. online, PDF at publisher, PDF preprint
- R. Mařík, Discrete singular functionals, Arch. Math. (Brno), Vol. 41 (2005), No. 3, 339-347. online
- R. Mařík, Oscillation of the half-linear PDE in general exterior domains—the variational approach, Nonlinear Anal. 60/3 (2005), 485-489. online, doi: 10.1016/j.na.2004.08.038, IF=0.519
- R. Mařík, Asymptotic estimates for PDE with p-Laplacian and damping, Electron. J. Qual. Theory Differ. Equ., No. 5. (2005), 1-6. online, PDF
- R. Mařík, Integral averages and oscillation of half-linear PDE, Appl. Math. Comp., Vol. 150 (2004), Issue 1, 69-87. online, doi: 10.1016/S0096-3003(03)00198-X
- R. Mařík, Riccati-type inequality and oscillation of half-linear PDE with damping, Electron. J. Differential Equations, Vol. 2004(2004), No. 11, 1-17. online, PDF
- R. Mařík, Positive solutions of inequality with p-Laplacian in exterior domains, Mathematica Bohemica, Vol. 127 (2002), No. 4, 597-604. online, PDF
- R. Mařík, Oscillation criteria for a class of nonlinear partial differential equations, Electron. J. Differential Equations, Vol. 2002(2002), No. 28, 1-10. online, PDF
- R. Mařík, Comparison theorems for half-linear second order difference equations, Arch. Math (Brno) 36 (2000), Proceedings of CDDE 2000 issue, 513-518. online
- R. Mařík, A half-linear differential equation and corresponding variational problem, Nonlinear Anal. 45/2 (2001), 203-211. online, PDF, IF=0.406
- R. Mařík, Focal points of half-linear second order differential equations, Diff. Eqs. Dyn. Syst. vol. 8. No. 2, (2000), 111-124. PDF preprint
- R. Mařík, Oscillation criteria for PDE with p-Laplacian via the Riccati technique, J. Math. Anal. Appl. 248 (2000), 290-308. online, PDF, IF=0.431
- R. Mařík, Hartman-Wintner type theorem for PDE with p-Laplacian, Electron. J. Differential Equations Proc. 6th Coll. QTDE 2000, No. 18, 1-7. online, PDF
- O. Došlý, R. Mařík, Nonexistence of the positive solutions of partial differential equations with p-Laplacian, Acta Math. Hungar. 90 (1-2) (2001), 89-107. PDF, IF=0.184
- R. Mařík, Oscillation criteria for Schroedinger PDE, Adv. Math. Sci. Appl. No. 2, Vol. 10 (2000), 495-511. PDF preprint
- R. Mařík, Nonnegativity of functionals corresponding to the second order half-linear differential equation, Arch. Math (Brno) 35 (1999), 155-164. online
- R. Mařík, On p-degree functionals with one free end point, Proc. Int. Sci. Conf. Math. Žilina (1998), 183-188. PDF preprint
Other publications
- Oscillation theory of partial differential equations with p-Laplacian, Mendel university (2008) 103 pages. Folia. ISBN 978-80-7375-215-6. PDF
Textbooks
- Differential and difference equations (Diferenciální a diferenční rovnice), textbook in Czech, Mendel University Brno (2004), 79 pages.
- Differential equations and autonomous systems (Diferenciální rovnice a autonomní systémy), textbook in Czech, Mendel University Brno (2009).PDF
Electronic textbooks in English
Other publications
- Half-linear differential equations, PhD. thesis, Masaryk Univ. Brno (2000), 72 pages.
- Bessel functions, thesis, Masaryk Univ. Brno (1997), in Czech.
- Tvorba interaktivních pdf testů pomocí programu AcroTeX. Department of Mathematics Report Series. 2005. No. 13, p. 111-114. In Czech.
- Pojďte pane, budeme si hrát (… s PDF). Mařík, Robert - Tihlaříková, Miroslava, In Proceedings of 7th International Conference APLIMAT 2008 - Part IV Open source Software in Research and Education. Bratislava: Department of Mathematics, Faculty of Mechanical Engineering, Slovak University of Technology, 2008, s. 63-73.
- Vkládání JavaScriptů pdfLaTeXem prakticky. Zpravodaj Československého sdružení uživatelů TeXu. 2007. sv. 2, č. 2, s. 72-83.
- LaTeX packages jeopardy, fancytooltips, mfpic4ode, OCGtools
- OpenSource versus proprietární software ve výuce a tvorbě výukových materiálů, Sborník 6. ročníku konference o elektronické podpoře výuky SCO 2009, s. 99-104.
- Oslí okénka v PDF, Zpravodaj Československého sdružení uživatelů TeXu. 2009. sv. 19, č. 1-2, s. 7-13.
- Mathematical Assistant on Web - skládanka ze svobodných matematických programů, In Otvorený softvér vo vzdelávaní, výskume a v IT riešeniach. s. 61-68. online.
- Support for differential equations in Sage
- Matematický program Sage, Matematika - fyzika - informatika 20 No. 2 (2010), 119-127.
Conferences
- Equadiff 9, Brno, August 1997
- Int. Scientific Conference of Mathematics, Zilina (SL), July 1998 - Half-linear differential equation and corresponding $p$-degree functional.
- Workshop on Qualitative Theory of Differential Equations, Brno, September 1998 - Half-linear differential equation and corresponding $p$-degree functional.
- 1. seminar of Center of Applied Mathematics, Plzen, May 1999 - Oscillation criteria for Schroedinger PDE.
- Boruvka Mathematical Symposium, Valtice, June 1999 poster - Oscillation criteria for Schroedinger PDE.
- 6. Colloq. Qual. Theory of Diff. Eqs., Szeged (HU), August 1999 - Oscillation criteria for Schroedinger PDE.
- 3-rd World Congress of Nonlinear Analysts - WCNA, Catania (IT), July
- Oscillation criteria for equations with p-Laplacian.
- Colloqium of Differential and Difference Equations - CDDE, Brno, September 2000. Focal points of half-linear difference equations.
- Colloqium of Differential and Difference Equations - CDDE, Brno, September 2002. Integral averages and oscillation of half-linear PDE.
- Equadiff 11, Bratislava, August 2005, Riccati technique for half-linear PDE.
- Colloqium of Differential and Difference Equations - CDDE, Brno, September 2006, An age-structured model of cannibalism.
- 8. Colloq. Qual. Theory of Diff. Eqs., Szeged (HU), June 2007 - Ordinary differential equations in the oscillation theory of partial half-linear differential equation.
- Conference on Differential and Difference Equations and Applications 2008 (CDDEA 2008) Strečno, Slovak Republic, June 23 - 27, 2008, Oscillation of half-linear partial differential equation.
- Equadiff 12, Brno, July 2009, Oscillation of PDE with p-Laplacian.
- International Conference on Difference Equations and Applications (ICDEA09) - October 19 - October 23, 2009, Estoril, Portugal.
- Conference on Differential and Difference Equations and Applications, Rajecké Teplice, Slovak Republic, June 21 - 25, 2010, Conjugacy criteria for half-linear ODE in theory of PDE with generalized p-Laplacian and mixed powers
- Colloquium on Differential Equations and Integration Theory, October 14 – 17, 2010, Křtiny, Czech Republic, Picone type inequality for half-linear differential operators with anisotropic p-Laplacian
- 9. Colloq. Qual. Theory of Diff. Eqs., Szeged (HU), June 2011 Principal solutions of half-linear equation: yet another integral characterization
- International Conference on Difference Equations and Applications (ICDEA09) - July 2011, Trois Rivieres, Canada, Half-linear difference equations and the discrete $p$-degree functional.
- Conference on Differential and Difference Equations and Applications, Terchova, Slovak Republic, On constants in nonoscillation criteria for half-linear differential equations, June 2012
- Equadiff 13, Riccati technique for half-linear delay differential equation, Prague, Czech Republic, Summer 2013
- DFDE 2014 - The Seventh International Conference on Differential and Functional Differential Equations, Riccati equation method for second order neutral half-linear equations, Moscow, Russia, August 2014
- International Workshop on Differential Equations in Osaka 2014 Riccati differential equation and its generalizations: a real treasure in oscillation and comparison theory of second order linear and half-linear differential equations, Japan, Osaka, November 2014.
- Qualitative theory of ordinary differential equations in real domains and its applications, Oscillation and nonoscillation criteria for half-linear differential equations: exploring ”terra incognita” and the hunt for better oscillation constants, Research Institute for Mathematical Sciences (RIMS) Kyoto University, Kyoto, Japan, November 2014.
Conferences focused on education
- Using compuers in teaching mathematics (in Czech), České Budějovice, November 2005, Využití systému LaTeX ve výuce matematiky.
- Using computers in teaching mathematics (in Czech), České Budějovice, November 2007, LaTeXem hravě.
- Aplimat 2008, February 2008, Bratislava, Pojďte pane, budeme si hrát (… s PDF).
- SCO (Sharable Content Objects) 2008, June 2008, Brno, Systém pro online výpočty v prostředí WWW
- Aplimat 2009, February 2009, Bratislava Mathematical Assistant on Web.
- SCO (Sharable Content Objects) 2009, June 2009, Brno, OpenSource versus proprietární software ve výuce a tvorbě výukových materiálů
Talks on seminars
- Seminar of differential equations, Masaryk Univ. Brno, fall 1998 and spring 1999, Nonnegativity of p-degree functionals and Oscillation properties of the partial differential equations of elliptic type, Czech
- Mathematical Institute at Hungarian Academy of Sciences: Budapest, April 1999 - 2 talks
- Seminar of differential equations, Masaryk Univ. Brno, Riccati transformation in the oscillation theory of PDE - radially nonsymetric criteria, 28.04.2003, in Czech
- Seminář katedry matematiky Ped. F. MU v Brně, Tvorba interaktivních matematických kvízů (ukázky, možnosti, návody a zkušenosti s programem AcroTeX), 16.11.2005, in Czech
- Seminar of differential equations, Masaryk Univ. Brno, Oscilační kriteria pro parciální diferenciální rovnice s p-Laplaciánem, 7.4.2008, in Czech
- Seminář katedry matematiky Ped. F. MU v Brně, Symbolické výpočty online, 22.10.2008, in Czech
- Odborný seminář z cyklu Aplikace matematických metod, Ekonomická fakulta VŠB v Ostravě, Proprietární versus OpenSource software ve výuce matematiky, 26.3.2009, in Czech
- Seminar of differential equations, Masaryk Univ. Brno, Oscillation criteria for half-linear neutral differential equation, 28.04.2014, in Czech
Presentations/prezentace
- Některé mé prezentace jsou dostupné zde