doc. Mgr. Zdeněk Opluštil, Ph.D.
E-mail:   oplustil@fme.vutbr.cz  Dept.:   Institute of Mathematics Dept. of Mathematical Analysis Position:   Associate Professor Room:   A1/1825

Supervised courses:

• Mathematics II-B (BM)
• Mathematics II-B (BM-K)
• Partial Differential Equations (SPD)

Publications:

• LOMTATIDZE, A.; OPLUŠTIL, Z.:
  Fredholm alternative for the second-order singular Dirichlet problem, Springer
  journal article in Web of Science
• OPLUŠTIL, Z.:
  Solvability of a nonlocal boundary value problem for linear functional differential equations,
  Advances in Difference Equations, Vol.2013, (2013), No.1, pp.1-19, ISSN 1687-1847, Springer
  journal article - other
• OPLUŠTIL, Z.; ŠREMR, J.:
  On oscillations of solutions to second-order linear delay differential equations,
  Georgian Mathematical Journal, Vol.2013 (20), (2013), No.1, pp.65-94, ISSN 1072-947X, Springer Verlag
  journal article - other
• OPLUŠTIL, Z.:
  Oscillatory criteria for two-dimensional system of difference equations,
  Tatra Mountains Mathematical Publications, Vol.48, (2011), No.7, pp.153-163, ISSN 1210-3195, Mathematical Institute, Slovak Academy of Science
  journal article - other
• OPLUŠTIL, Z.; ŠREMR, J.:
  Some oscillation criteria for the second-order linear delay differential equation,
  Mathematica Bohemica, Vol.136, (2011), No.2, pp.195-204, ISSN 0862-7959, Institute of Mathematics, Academy of Sciences of the Czech Republic
  journal article - other
• OPLUŠTIL, Z.; LOMTATIDZE, A.; ŠREMR, J.:
  Nonpositive solutions of one functional differential inequality,
  Nonlinear Oscillations, Vol.2009 (12), (2009), No.4, pp.474-509, ISSN 1536-0059, Springer Verlag
  journal article - other
• OPLUŠTIL, Z.:
  Solvability of a linear non-local boundary value problem for nonlinear functional differential equations,
  Tatra Mountains Mathematical Publications, Vol.43, (2009), No.1, pp.189-201, ISSN 1210-3195, Mathematical Institute, Slovak Academy of Science
  journal article - other
• OPLUŠTIL, Z.; ŠREMR, J.:
  On a non-local boundary value problem for linear functional differential equations,
  Electronic Journal of Qualitative Theory of Differential Equations, Vol.2009, (2009), No.36, pp.1-13, ISSN 1417-3875, Bolyai Institute, University of Szeged
  journal article - other
• OPLUŠTIL, Z.; LOMTATIDZE, A.; ŠREMR, J.:
  Solvability conditions for a nonlocal boundary value problem for linear functional differential equations,
  Fasciculi Mathematici, Vol.2009, (2009), No.41, pp.81-96, ISSN 0044-4413, Poznan University of Technology
  journal article - other
• OPLUŠTIL, Z.:
  On constant sign solutions (nonpositive) of certain functional differential inequality,
  AIP conference proceedings, Vol.2009, (2009), No.1124, pp.274-283, ISSN 0094-243X, American Institute of Physics
  journal article - other
  akce: MATHEMATICAL MODELS IN ENGINEERING, BIOLOGY AND MEDICINE: International Conference on Boundary Value Problems: Mathematical Models in Engineering, Biology and Medicine, Santiago de Compostela, 16.09.2009-19.09.2009
• OPLUŠTIL, Z.:
  New solvability conditions for a non-local boundary value problem for nonlinear functional differential equations,
  Nonlinear Oscillations, Vol.2008 (11), (2008), No.3, pp.384-406, ISSN 1536-0059, Springer Verlag
  journal article - other
• OPLUŠTIL, Z.:
  On compositions of fractional derivatives,
  5. Konference o matematice a fyzice na vysokých školách technických, pp.231-240, ISBN 978-80-7231-274-0, (2007), Univerzita obrany Brno
  conference paper
  akce: 5. konference o matematice a fyzice na vysokých školách technických s mezinárodní účastí, Univerzita obrany, Brno, 13.09.2007-13.09.2007
• OPLUŠTIL, Z.:
  O nelokální okrajové úloze pro lineární funkcionální diferenciální rovnici prvního řádu,
  Sborník z 15. semináře Moderní metody matematického inženýrství, pp.171-345, ISBN 80-248-1224-X, (2006), VŠB - TECHNICKÁ UNIVERZITA OSTRAVA
  conference paper
  akce: 15. ročník semináře Moderní matematické metody v inženýrství 3mí, Dolní Lomná, Jestřábský potok, 29.05.2006-31.05.2006
• OPLUŠTIL, Z.; LOMTATIDZE, A.:
  On nonnegative solutions of a certain boundary value problem for first order linear functional differential equations.,
  Electronic Journal of Qualitative Theory of Differential Equations, Vol.2003, (2004), No.16, pp.1-21, ISSN 1417-3875, Univ. Szeged
  journal article - other
  akce: Seventh Colloquium on the Qualitative Theory of Differential Equations, Szeged, 14.07.2003-18.07.2003
• OPLUŠTIL, Z.; POSPÍŠIL, Z.:
  An Oscillation Criterion for a Dynamic Sturm-Liouville Equation,
  PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON DIFFERENCE EQUATIONS: NEW PROGRESS IN DIFFERENCE EQUATIONS, pp.317-324, ISBN 0-415-31675-8, (2004), CRC Press, Boca Raton, Florida, USA
  conference paper
  akce: Sixth International Conference on Differenca Equations and Applications, Augsburg, 30.07.2001-03.08.2001

List of publications at Portal BUT

Abstracts of most important papers:

• OPLUŠTIL, Z.:
  Solvability of a nonlocal boundary value problem for linear functional differential equations,
  Advances in Difference Equations, Vol.2013, (2013), No.1, pp.1-19, ISSN 1687-1847, Springer
  journal article - other
  In the paper, the problem on the existence and uniqueness of a solution to the nonlocal problem u'(t)=l(u)(t)+q(t), u(a)=h(u)+c is studied. They are found conditions guaranteeing the unique solvability of considered problem.
• OPLUŠTIL, Z.; ŠREMR, J.:
  On oscillations of solutions to second-order linear delay differential equations,
  Georgian Mathematical Journal, Vol.2013 (20), (2013), No.1, pp.65-94, ISSN 1072-947X, Springer Verlag
  journal article - other
  New oscillation criteria are proved for second-order two-term linear delay differential equations with locally integrable coefficients and measurable delays. In particular, a suitable a priori lower bound of non-oscillatory solutions is found, which plays a crucial role in the proofs of the results obtained.
• OPLUŠTIL, Z.; ŠREMR, J.:
  Some oscillation criteria for the second-order linear delay differential equation,
  Mathematica Bohemica, Vol.136, (2011), No.2, pp.195-204, ISSN 0862-7959, Institute of Mathematics, Academy of Sciences of the Czech Republic
  journal article - other
  Some Wintner and Nehari type oscillation criteria are established for the second-order linear delay differential equation.
• OPLUŠTIL, Z.; LOMTATIDZE, A.; ŠREMR, J.:
  Nonpositive solutions of one functional differential inequality,
  Nonlinear Oscillations, Vol.2009 (12), (2009), No.4, pp.474-509, ISSN 1536-0059, Springer Verlag
  journal article - other
  In the paper, the effcient conditions are found guaranteeing that every solution of one functional differential equation are nonpositive.
• OPLUŠTIL, Z.; ŠREMR, J.:
  On a non-local boundary value problem for linear functional differential equations,
  Electronic Journal of Qualitative Theory of Differential Equations, Vol.2009, (2009), No.36, pp.1-13, ISSN 1417-3875, Bolyai Institute, University of Szeged
  journal article - other
  We establish new efficient conditions for the unique solvability of a non-local boundary value problem for first-order linear functional differential equations. Differential equations with argument deviations are also considered in which case further results are obtained.