Prof. RNDr. Roman Šimon Hilscher, DSc.
ŠIMON HILSCHER, Roman - ZEIDAN, Vera Michel.
Hamilton-Jacobi theory over time scales and applications to linear-quadratic problems. Nonlinear Analysis, Theory, Methods & Applications, Amsterdam, Elsevier Science Ltd., The Nederlands. ISSN 0362-546X, 2012, vol. 75, no. 2, pp. 932-950.
ŠIMON HILSCHER, Roman - ZEMÁNEK, Petr.
New results for time reversed symplectic dynamic systems and quadratic functionals. Electronic Journal of Qualitative Theory of Differential Equations, Szeged, Bolyai Institute, University of Szeged, Hungary. ISSN 1417-3875, 2012, vol. Neuveden, no. 15, pp. 1-11. Proc. Colloq. Qual. Theory Differ. Equ., Vol. 9, No. 15, 11 pp. (electronic), Electron. J. Qual. Theory Differ. Equ., 2012.
BOHNER, Martin - KRATZ, Werner - ŠIMON HILSCHER, Roman.
Oscillation and spectral theory for linear Hamiltonian systems with nonlinear dependence on the spectral parameter. Mathematische Nachrichten, Wiley Inter Science, Germany. ISSN 0025-584X, 2012.
DOŠLÝ, Ondřej - ÖZBEKLER, Abdullah - ŠIMON HILSCHER, Roman.
Oscillation criterion for half-linear differential equations with periodic coefficients. Journal of Mathematical Analysis and Applications, San Diego (USA), Elsevier Science, USA. ISSN 0022-247X, 2012, vol. 393, no. 2, pp. 360-366.
ŠIMON HILSCHER, Roman - ZEIDAN, Vera Michel.
Oscillation theorems and Rayleigh principle for linear Hamiltonian and symplectic systems with general boundary conditions. Applied Mathematics and Computation, Spojené státy americké, Elsevier, USA. ISSN 0096-3003, 2012, vol. 218, no. 17, pp. 8309-8328.
KRATZ, Werner - ŠIMON HILSCHER, Roman.
Rayleigh principle for linear Hamiltonian systems without controllability. ESAIM: Control, Optimisation and Calculus of Variations, Les Ulis, EDP Sciences, France. ISSN 1292-8119, 2012.
KRATZ, Werner - ŠIMON HILSCHER, Roman - ZEIDAN, Vera Michel.
Eigenvalue and oscillation theorems for time scale symplectic systems. International Journal of Dynamical Systems and Differential Equations, Ženeva, Indersci. Enterp. Ltd., Switzerland. ISSN 1752-3583, 2011, vol. 3, no. 1-2, pp. 84-131.
ŠIMON HILSCHER, Roman - ZEIDAN, Vera Michel.
First order conditions for generalized variational problems over time scales. Computers & Mathematics with Applications, Elsevier Science Ltd., USA. ISSN 0898-1221, 2011, vol. 62, no. 9, pp. 3490-3503.
ŠIMON HILSCHER, Roman.
On general Sturmian theory for abnormal linear Hamiltonian systems. In Proceedings of the 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications. Springfield, Missouri : AIMS (American Institute of Mathematical Sciences), 2011. ISBN 978-1-60133-007-9, pp. 684-691. 2010, Drážďany. Discrete Contin. Dynam. Systems, Suppl. 2011.
ŠIMON HILSCHER, Roman - ZEMÁNEK, Petr.
Overview of Weyl-Titchmarsh theory for second order Sturm-Liouville equations on time scales. Int. J. Difference Equ., Delhi, Research India Publications, India. ISSN 0973-6069, 2011, vol. 6, no. 1, pp. 39-51.
ŠIMON HILSCHER, Roman - ZEIDAN, Vera Michel.
Rayleigh principle for time scale symplectic systems and applications. Electronic Journal of Qualitative Theory of Differential Equations, Szeged, Hungary. ISSN 1417-3875, 2011, vol. 2011, no. 83, pp. 1-26.
ŠIMON HILSCHER, Roman.
Sturmian theory for linear Hamiltonian systems without controllability. Mathematische Nachrichten, Berlín, Wiley Inter Science, Germany. ISSN 0025-584X, 2011, vol. 284, no. 7, pp. 831-843.
ŠIMON HILSCHER, Roman - ZEMÁNEK, Petr.
Weyl-Titchmarsh theory for time scale symplectic systems on half line. Abstract and Applied Analysis, New York, Hindawi Publishing Corporation, USA. ISSN 1085-3375, 2011, vol. 2011, no. 738520, pp. 1-41.
Abstract Book of CDEIT 2010. Vyd. 1. Brno : Masarykova univerzita, 2010. 122 pp. ISBN 978-80-210-5289-5.
DOŠLÁ, Zuzana - MAŘÍK, Robert - ŠIMON HILSCHER, Roman - ŠREMR, Jiří - FIŠNAROVÁ, Simona - TVRDÝ, Milan - LEPKA, Karel.
Colloquium on Differential Equations and Integration Theory. 2010. CZE, Křtiny. 14.10.2010 - 17.10.2010, Worldwide Activity.
ŠIMON HILSCHER, Roman - ZEMÁNEK, Petr.
Friedrichs extension of operators defined by linear Hamiltonian systems on unbounded interval. Mathematica Bohemica, Praha, Matematický ústav AV ČR. ISSN 0862-7959, 2010, vol. 315, no. 2, pp. 209-222.
ŠIMON HILSCHER, Roman - ZEIDAN, Vera Michel.
Nabla time scale symplectic systems and related quadratic functionals. Differential Equations and Dynamical Systems, Springer India, India. ISSN 0971-3514, 2010, vol. 18, no. 1-2, pp. 163-198.
ŠIMON HILSCHER, Roman - ZEIDAN, Vera Michel.
Reid roundabout theorems for time scale symplectic systems. In Discrete Dynamics and Difference Equations. Vyd. 1. Londýn : World Scientific Publishing Co., 2010. ISBN 978-981-4287-64-7, pp. 267-288. 2007, Lisbon.
ŠIMON HILSCHER, Roman - ZEIDAN, Vera Michel.
Symmetric three-term recurrence equations and their symplectic structure. Advances in Difference Equations, New York, Hindawi Publishing Corporation, USA. ISSN 1687-1839, 2010, vol. 2010, no. ID 626942, 17 pp.
ŠIMON HILSCHER, Roman - ZEIDAN, Vera Michel.
Symplectic structure of Jacobi systems on time scales. International Journal of Difference Equations, Delhi (Indie), Research India Publications, India. ISSN 0973-6069, 2010, vol. 5, no. 1, pp. 55-81.
ŠIMON HILSCHER, Roman.
A note on the time scale calculus of variations problems. Ulm : University of Ulm, 2009. 8 pp. Ulmer Seminare 14.
ŠIMON HILSCHER, Roman - ZEMÁNEK, Petr.
Definiteness of quadratic functionals for Hamiltonian and symplectic systems: A survey. International Journal of Difference Equations, Delhi (Indie), Research India Publications, India. ISSN 0973-6069, 2009, vol. 4, no. 1, pp. 49-67.
ŠIMON HILSCHER, Roman - KRATZ, Werner - ZEIDAN, Vera Michel.
Differentiation of solutions of dynamic equations on time scales with respect to parameters. Advances in Dynamical Systems and Applications, Delhi (Indie), Research India Publications, India. ISSN 0973-5321, 2009, vol. 4, no. 1, pp. 35-54.
ŠIMON HILSCHER, Roman.
Eigenvalue, oscillation, and variational results for time scale symplectic systems. 2009.
ŠIMON HILSCHER, Roman - DOŠLÝ, Ondřej - ČERMÁK, Jan - DIBLÍK, Josef - DOŠLÁ, Zuzana - HAKL, Robert - LEPKA, Karel - LOMTATIDZE, Alexander - ŘEHÁK, Pavel - ŠMARDA, Zdeněk - SVOBODA, Zdeněk - FIŠNAROVÁ, Simona.
International Conference on Differential Equations and Their Applications (Equadiff 12). 2009. CZE, Brno. 20.7.2009 - 24.7.2009, Worldwide Activity.
ŠIMON HILSCHER, Roman - ZEIDAN, Vera Michel.
Multiplicities of focal points for discrete symplectic systems: revisited. Journal of Difference Equations and Applications, Taylor and Francis, Great Britain. ISSN 1023-6198, 2009, vol. 15, no. 10, pp. 1001-1010.
ŠIMON HILSCHER, Roman - ZEIDAN, Vera.
Oscillation results for time scale symplectic systems. In Proceedings of the 14th International Conference on Difference Equations and Applications. Istanbul : Ugur-Bahcesehir University Publishing Company, 2009. ISBN 978-975-6437-80-3, pp. 203-210. 2008, Istanbul.
ŠIMON HILSCHER, Roman - ZEIDAN, Vera Michel.
Picone type identities and definiteness of quadratic functionals on time scales. Applied Mathematics and Computation, Elsevier, USA. ISSN 0096-3003, 2009, vol. 215, no. 7, 2425–2437-13 pp.
ŠIMON HILSCHER, Roman - ZEMÁNEK, Petr.
Trigonometric and hyperbolic systems on time scales. Dynamic Systems and Applications, Atlanta, USA, Dynamic Publishers,Inc., USA. ISSN 1056-2176, 2009, vol. 18, no. 3-4, pp. 483-506.
ŠIMON HILSCHER, Roman - ZEIDAN, Vera.
Weak maximum principle and accessory problem for control problems on time scales. Nonlinear Analysis, USA. ISSN 0362-546X, 2009, vol. 70, no. 9, pp. 3209-3226.
HILSCHER, Roman - ZEIDAN, Vera.
Applications of time scale symplectic systems without normality. Journal of Mathematical Analysis and Applications, San Diego (USA), Elsevier Science, USA. ISSN 0022-247X, 2008, vol. 340, no. 1, pp. 451-465.
HILSCHER, Roman - ZEIDAN, Vera Michel.
Riccati equations for abnormal time scale quadratic functionals. Journal of Differential Equations, San Diego (USA), Elsevier Science, USA. ISSN 0022-0396, 2008, vol. 244, no. 6, pp. 1410-1447.
HILSCHER, Roman - TISDELL, Christopher C..
Terminal value problems for first and second order nonlinear equations on time scales. Electronic Journal of Differential Equations, San Marcos, TX 78666, USA, Texas State University - San Marcos, USA. ISSN 1072-6691, 2008, vol. 2008, no. 68, pp. 1-21.
HILSCHER, Roman - ZEIDAN, Vera.
Time scale embedding theorem and coercivity of quadratic functionals. Analysis (Munich), Mnichov, Oldenbourg Wissenschaftsverlag, Germany. ISSN 0174-4747, 2008, vol. 28, no. 1, pp. 1-28.
HILSCHER, Roman - ZEIDAN, Vera.
Extension of discrete LQR-problem to symplectic systems. International Journal of Difference Equations, Delhi (Indie), Research India Publications, India. ISSN 0973-6069, 2007, vol. 2, no. 2, pp. 197-208.
HILSCHER, Roman - ZEIDAN, Vera.
Legendre, Jacobi, and Riccati type conditions for time scale variational problem with application. Dynamic Systems and Applications, Atlanta, USA, Dynamic Publishers,Inc., USA. ISSN 1056-2176, 2007, vol. 16, no. 3, pp. 451-480.
HILSCHER, Roman - RŮŽIČKOVÁ, Viera.
Perturbation of nonnegative time scale quadratic functionals. In Difference Equations, Special Functions, and Orthogonal Polynomials. Londýn : World Scientific, 2007. ISBN 978-981-270-643-0, pp. 266-275. 2005, Mnichov.
HILSCHER, Roman - RŮŽIČKOVÁ, Viera.
Perturbation of time scale quadratic functionals with variable endpoints. Advances in Dynamical Systems and Applications, Delhi (Indie), Research India Publications, India. ISSN 0973-5321, 2007, vol. 2, no. 2, pp. 207-224.
ŠIMON HILSCHER, Roman.
Přednášky MB102 Matematika II. Brno : Fakulta informatiky, Masarykova univerzita, 2007. 144 pp.
DOŠLÝ, Ondřej - DOŠLÁ, Zuzana - ŘEHÁK, Pavel - HILSCHER, Roman - BARTUŠEK, Miroslav - POSPÍŠIL, Zdeněk - SCHWABIK, Štefan.
Colloquium on Differential and Difference Equations. 2006. CZE, Brno. 5.9.2006 - 8.9.2006, European Activity. Konference věnovaná profesoru Jaroslavu Kurzweilovi u příležitosti jeho 80. narozenin.
HILSCHER, Roman.
Comparison results for solutions of time scale matrix Riccati equations and inequalities. The Australian Journal of Mathematical Analysis and Applications, Victoria, Austrálie, Australian Internet Publishing, Australia. ISSN 1449-5910, 2006, vol. 3, no. 2, pp. Article 13, 1-15.
HILSCHER, Roman - ZEIDAN, Vera.
Coupled intervals for discrete symplectic systems. Linear Algebra and its Applications, USA, Elsevier Science, USA. ISSN 0024-3795, 2006, vol. 419, no. 2-3, pp. 750-764.
HILSCHER, Roman - RŮŽIČKOVÁ, Viera.
Implicit Riccati equations and quadratic functionals for discrete symplectic systems. International Journal of Difference Equations, Delhi (Indie), Research India Publications, India. ISSN 0973-6069, 2006, vol. 1, no. 1, pp. 135-154.
ŠIMON HILSCHER, Roman.
Přednášky MB101 Matematika I. Brno : Fakulta informatiky, Masarykova univerzita, 2006. 157 pp.
HILSCHER, Roman - RŮŽIČKOVÁ, Viera.
Riccati inequality and other results for discrete symplectic systems. Journal of Mathematical Analysis and Applications, San Diego (USA), Elsevier Science, USA. ISSN 0022-247X, 2006, vol. 322, no. 2, pp. 1083-1098.
HILSCHER, Roman - ZEIDAN, Vera.
Time scale symplectic systems without normality. Journal of Differential Equations, San Diego (USA), Elsevier Science, USA. ISSN 0022-0396, 2006, vol. 230, no. 1, pp. 140-173.
BOHNER, Martin - HILSCHER, Roman.
An eigenvalue problem for linear Hamiltonian dynamic systems. Fasciculi Mathermatici, Poznaň, Polsko, Politechnika Poznaňska, Institut Mat., Poland. ISSN 0044-4413, 2005, vol. 35, no. 1, pp. 35-49.
HILSCHER, Roman - ZEIDAN, Vera.
Nonnegativity and positivity of quadratic functionals in the discrete calculus of variations: Survey. Journal of Difference Equations and Applications, Taylor and Francis, Great Britain. ISSN 1023-6198, 2005, vol. 11, no. 9, pp. 857-875.
HILSCHER, Roman - ZEIDAN, Vera.
Solvability of the discrete LQR-problem under minimal assumptions. In Difference Equations and Discrete Dynamical Systems. London : World Scientific Publishing Co., 2005. ISBN 981-256-520-5, pp. 273-282. 2004, Los Angeles.
HILSCHER, Roman - ZEIDAN, Vera.
Calculus of variations on time scales: weak local piecewise C1rd solutions with variable endpoints. Journal of Mathematical Analysis and Applications, San Diego (USA), Elsevier Science, USA. ISSN 0022-247X, 2004, vol. 289, no. 1, pp. 143-166.
HILSCHER, Roman - ZEIDAN, Vera.
Coupled intervals in the discrete optimal control. Journal of Difference Equations and Applications, Taylor and Francis, Great Britain. ISSN 1023-6198, 2004, vol. 10, no. 2, pp. 151-186.
HILSCHER, Roman - ZEIDAN, Vera.
Discrete quadratic functionals with jointly varying endpoints via separable endpoints. In Proceedings of the Sixth International Conference on Difference Equations. Boca Raton : Chapman & Hall/CRC, 2004. ISBN 0-415-31675-8, pp. 461-470. 2001, Augsburg.
HILSCHER, Roman - ZEIDAN, Vera.
Equivalent conditions to the nonnegativity of a quadratic functional in discrete optimal control. Mathematische Nachrichten, Berlin, WILEY-VCH Verlag, Germany. ISSN 0025-584X, 2004, vol. 266, no. 1, pp. 48-59.
DOŠLÝ, Ondřej - HILSCHER, Roman.
A class of Sturm-Liouville difference equations: (non)oscillation constants and property BD. Comput Math. Appl., USA. ISSN 0898-1221, 2003, vol. 45, no. 1, pp. 961-981.
HILSCHER, Roman - ZEIDAN, Vera.
A remark on discrete quadratic functionals with separable endpoints. Rocky Mountain Journal of Mathematics, USA. ISSN 0035-7596, 2003, vol. 33, no. 4, pp. 1337-1351.
BOHNER, Martin - DOŠLÝ, Ondřej - HILSCHER, Roman - KRATZ, Werner.
Diagonalization approach to discrete quadratic functionals. Archives of Inequalities and Applications, Atlanta, Georgia, USA, Dynamic Publishers, Inc., USA. ISSN 1542-6149, 2003, vol. 1, no. 2, pp. 261-274.
HILSCHER, Roman - ZEIDAN, Vera.
Nonnegativity of a discrete quadratic functional in terms of the (strengthened) Legendre and Jacobi conditions. Computers & mathematics with applications, New York, Pergamon Press, USA. ISSN 0097-4943, 2003, vol. 45, no. 6-9, pp. 1369-1383.
DOŠLÝ, Ondřej - HILSCHER, Roman - ZEIDAN, Vera.
Nonnegativity of discrete quadratic functionals corresponding to symplectic difference systems. Linear Algebra and its Applications, USA, Elsevier Science, USA. ISSN 0024-3795, 2003, vol. 375, no. 1.12.2003, pp. 21-44.
HILSCHER, Roman - ŘEHÁK, Pavel.
Riccati inequality, disconjugacy, and reciprocity principle for linear Hamiltonian dynamic systems. Dynamic Systems and Applications, Atlanta, USA, Dynamic Publishers,Inc., USA. ISSN 1056-2176, 2003, vol. 12, no. 1-2, pp. 171-189.
HILSCHER, Roman - ZEIDAN, Vera.
Symplectic difference systems: variable stepsize discretization and discrete quadratic functionals. Linear Algebra and its Applications, USA, Elsevier Science, USA. ISSN 0024-3795, 2003, vol. 367, no. 1, pp. 67-104.
DOŠLÝ, Ondřej - HILGER, Stefan - HILSCHER, Roman.
Symplectic dynamic systems. In Advances in Dynamic Equations on Time Scales, M. Bohner and A. Peterson, editors. Boston : Birkhauser, 2003. Normální knížka, ISBN 0-8176-4293-5, pp. 345-392.
HILSCHER, Roman.
A time scales version of a Wirtinger type inequality and applications. Journal of Computational and Applied Mathematics, Elsevier Science, USA. ISSN 0377-0427, 2002, vol. 141, no. 1-2, pp. 219-226.
HILSCHER, Roman - ZEIDAN, Vera.
Coupled intervals in the discrete calculus of variations: necessity and sufficiency. Journal of Mathematical Analysis and Applications, USA, Acad.Press, USA. ISSN 0022-247X, 2002, vol. 276, no. 1, pp. 396-421.
HILSCHER, Roman - ZEIDAN, Vera.
Discrete optimal control: second order optimality conditions. Journal of Difference Equations and Applications, Taylor and Francis, Great Britain. ISSN 1023-6198, 2002, vol. 8, no. 10, pp. 875-896.
HILSCHER, Roman - ZEIDAN, Vera.
Second order sufficiency criteria for a discrete optimal control problem. Journal of Difference Equations and Applications, Taylor and Francis, Great Britain. ISSN 1023-6198, 2002, vol. 8, no. 6, pp. 573-602.
DOŠLÝ, Ondřej - HILSCHER, Roman.
Disconjugacy, transformations and quadratic functionals for symplectic dynamic systems on time scales. J. Difference Equations Appl., San Diego, USA. ISSN 1023-6198, 2001, vol. 7, no. 3, pp. 265-294.
HILSCHER, Roman.
Discrete spectra criteria for certain classes of singular diffferential and difference operators. Computers & mathematics with applications, New York, Pergamon Press, USA. ISSN 0097-4943, 2001, vol. 42, no. 3-5, pp. 465-476.
HILSCHER, Roman.
Inhomogeneous quadratic functionals on time scales. Journal of Mathematical Analysis and Applications, USA, Acad.Press, USA. ISSN 0022-247X, 2001, vol. 253, no. 2, pp. 473-481.
DOŠLÝ, Ondřej - BOHNER, Martin - HILSCHER, Roman.
Linear Hamiltonian dynamic systems on time scales: Sturmian property of principal solution. Nonlin. Anal., Atlanta, USA. ISSN 0362-546X, 2001, vol. 47, no. 2, pp. 849-859.
HILSCHER, Roman.
Positivity of quadratic functionals on time scales: necessity. Mathematische Nachrichten, Berlin, WILEY-VCH Verlag, Germany. ISSN 0025-584X, 2001, vol. 226, no. 1, pp. 85-98.
HILSCHER, Roman.
Reid roundabout theorem for symplectic dynamic systems on time scales. Applied Mathematics and Optimization, New York, Springer-Verlag, USA. ISSN 0095-4616, 2001, vol. 43, no. 2, pp. 129-146.
HILSCHER, Roman - ZEIDAN, Vera.
Discrete optimal control: the accessory problem and necessary optimality conditions. Journal of Mathematical Analysis and Applications, San Diego (USA), Academic Press, USA. ISSN 0022-247X, 2000, vol. 243, no. 2, pp. 429-452.
HILSCHER, Roman.
Linear Hamiltonian systems on time scales: positivity of quadratic functionals. Mathematical and Computer Modelling, Elsevier Science, USA. ISSN 0895-7177, 2000, vol. 32, no. 5-6, pp. 507-527.
HILSCHER, Roman.
On disconjugacy for vector linear Hamiltonian systems on time scales. In Communications in Difference Equations: Proceedings of the Fourth International Conference on Difference Equations. Amsterdam : Gordon and Breach, 2000. ISBN 90-5699-688-6, pp. 181-188. 1998, Poznan.
HILSCHER, Roman.
Spectral properties of general self-adjoint, even order differential operators. Mathematica Slovaca, Bratislava, Slovak Academy of Sciences, Slovakia. ISSN 0139-9918, 2000, vol. 50, no. 2, pp. 165-186.
HILSCHER, Roman.
Disconjugacy of symplectic systems and positive definiteness of block tridiagonal matrices. Rocky Mountain Journal of Mathematics, USA. ISSN 0035-7596, 1999, vol. 29, no. 4, pp. 1301-1319.
DOŠLÝ, Ondřej - HILSCHER, Roman.
Linear Hamiltonian difference systems: Transformations, recessive solutions, generalized reciprocity. Dyn. Syst. Appl., USA. ISSN 1056-2176, 1999, vol. 8, no. 2, pp. 401-420.
HILSCHER, Roman.
Linear Hamiltonian systems on time scales: transformations. Dynamic Systems and Applications, Atlanta, USA, Dynamic Publishers,Inc., USA. ISSN 1056-2176, 1999, vol. 8, no. 3-4, pp. 489-501.
DOŠLÝ, Ondřej - HILSCHER, Roman.
Spectral properties of fourth order differential operators. Mathematica Bohemica : časopis pro pěstování matematiky, Praha, Matematický ústav AV ČR. ISSN 0862-7959, 1997, vol. 122, no. 3, pp. 153-168.
