## Šimon Hilscher, Roman

Compute Distance To:
 Author ID: simon-hilscher.roman Published as: Šimon Hilscher, Roman; Hilscher, Roman; Hilscher, R.; Šimon Hilscher, R. more...less Homepage: https://www.math.muni.cz/~hilscher/ External Links: MGP · ORCID · dblp
 Documents Indexed: 105 Publications since 1997, including 2 Books Reviewing Activity: 166 Reviews Co-Authors: 12 Co-Authors with 84 Joint Publications 302 Co-Co-Authors
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### Co-Authors

 21 single-authored 34 Zeidan, Vera Michel 18 Šepitka, Peter 11 Zemánek, Petr 9 Došlý, Ondřej 6 Kratz, Werner 5 Bohner, Martin J. 3 Růžičková, Viera 2 Dřímalová, Iva 2 Elyseeva, Julia V. 1 Özbekler, Abdullah 1 Řehák, Pavel 1 Siegmund, Stefan 1 Stehlík, Petr 1 Tisdell, Christopher C.
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### Serials

 10 Journal of Difference Equations and Applications 9 Journal of Mathematical Analysis and Applications 9 Journal of Differential Equations 8 Linear Algebra and its Applications 6 Mathematische Nachrichten 6 Dynamic Systems and Applications 4 Computers & Mathematics with Applications 4 Applied Mathematics and Computation 4 Electronic Journal of Qualitative Theory of Differential Equations 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Advances in Difference Equations 2 Rocky Mountain Journal of Mathematics 2 Mathematica Bohemica 2 Journal of Dynamics and Differential Equations 1 Applied Mathematics and Optimization 1 Archivum Mathematicum 1 Fasciculi Mathematici 1 Journal of Computational and Applied Mathematics 1 Mathematica Slovaca 1 Mathematical and Computer Modelling 1 SIAM Journal on Matrix Analysis and Applications 1 Electronic Journal of Differential Equations (EJDE) 1 Discrete and Continuous Dynamical Systems 1 Differential Equations and Dynamical Systems 1 Abstract and Applied Analysis 1 Analysis (München) 1 Archives of Inequalities and Applications 1 The Australian Journal of Mathematical Analysis and Applications 1 International Journal of Difference Equations 1 International Journal of Dynamical Systems and Differential Equations 1 Springer Proceedings in Mathematics & Statistics 1 Pathways in Mathematics
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### Fields

 61 Ordinary differential equations (34-XX) 61 Difference and functional equations (39-XX) 41 Dynamical systems and ergodic theory (37-XX) 22 Calculus of variations and optimal control; optimization (49-XX) 21 Systems theory; control (93-XX) 11 Linear and multilinear algebra; matrix theory (15-XX) 5 Operator theory (47-XX) 4 Operations research, mathematical programming (90-XX) 2 Real functions (26-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Differential geometry (53-XX) 1 Numerical analysis (65-XX) 1 Mechanics of particles and systems (70-XX)

### Citations contained in zbMATH Open

95 Publications have been cited 858 times in 289 Documents Cited by Year
Calculus of variations on time scales: Weak local piecewise $$C_{\text{rd}}^{1}$$ solutions with variable endpoints. Zbl 1043.49004
Hilscher, Roman; Zeidan, Vera
2004
Weak maximum principle and accessory problem for control problems on time scales. Zbl 1157.49030
Hilscher, Roman; Zeidan, Vera
2009
Disconjugacy, transformations and quadratic functionals for symplectic dynamic systems on time scales. Zbl 0989.34027
Došlý, Ondřej; Hilscher, Roman
2001
Sturmian theory for linear Hamiltonian systems without controllability. Zbl 1218.34038
Šimon Hilscher, Roman
2011
Second order sufficiency criteria for a discrete optimal control problem. Zbl 1010.49020
Hilscher, Roman; Zeidan, Vera
2002
Minimal principal solution at infinity for nonoscillatory linear Hamiltonian systems. Zbl 1305.34053
Šepitka, Peter; Šimon Hilscher, Roman
2014
Reid roundabout theorem for symplectic dynamic systems on time scales. Zbl 0990.39017
Hilscher, R.
2001
Symplectic difference systems: Variable stepsize discretization and discrete quadratic functionals. Zbl 1021.39008
Hilscher, Roman; Zeidan, Vera
2003
A time scales version of a Wirtinger-type inequality and applications. Zbl 1025.26012
Hilscher, Roman
2002
Discrete optimal control: Second order optimality conditions. Zbl 1010.49021
Hilscher, Roman; Zeidan, Vera
2002
Rayleigh principle for linear Hamiltonian systems without controllability. Zbl 1254.34120
Kratz, Werner; Šimon Hilscher, Roman
2012
Comparative index and Sturmian theory for linear Hamiltonian systems. Zbl 1375.34052
Šepitka, Peter; Šimon Hilscher, Roman
2017
Weyl-Titchmarsh theory for discrete symplectic systems with general linear dependence on spectral parameter. Zbl 1312.39011
Šimon Hilscher, Roman; Zemánek, Petr
2014
Applications of time scale symplectic systems without normality. Zbl 1145.39006
Hilscher, Roman; Zeidan, Vera
2008
Principal solutions at infinity of given ranks for nonoscillatory linear Hamiltonian systems. Zbl 1348.37091
Šepitka, Peter; Šimon Hilscher, Roman
2015
Riccati equations for abnormal time scale quadratic functionals. Zbl 1355.49031
Hilscher, Roman; Zeidan, Vera
2008
Nonnegativity and positivity of quadratic functionals in discrete calculus of variations: survey. Zbl 1098.49025
Hilscher, Roman; Zeidan, Vera
2005
Limit point and limit circle classification for symplectic systems on time scales. Zbl 1334.34197
Šimon Hilscher, Roman; Zemánek, Petr
2014
Riccati inequality and other results for discrete symplectic systems. Zbl 1103.39020
Hilscher, Roman; Růžičková, Viera
2006
Time scale embedding theorem and coercivity of quadratic functionals. Zbl 1136.49017
Hilscher, Roman; Zeidan, Vera
2008
Principal and antiprincipal solutions at infinity of linear Hamiltonian systems. Zbl 1329.34024
Šepitka, Peter; Šimon Hilscher, Roman
2015
On general Sturmian theory for abnormal linear Hamiltonian systems. Zbl 1306.34051
Šimon Hilscher, Roman
2011
Time scale symplectic systems without normality. Zbl 1104.37037
Hilscher, Roman; Zeidan, Vera
2006
Oscillation and spectral theory for linear Hamiltonian systems with nonlinear dependence on the spectral parameter. Zbl 1254.34119
Bohner, Martin; Kratz, Werner; Šimon Hilscher, Roman
2012
Disconjugacy of symplectic systems and positive definiteness of block tridiagonal matrices. Zbl 0956.39010
Hilscher, Roman
1999
Discrete spectra criteria for certain classes of singular differential and difference operators. Zbl 1008.39011
Hilscher, R.
2001
Linear Hamiltonian dynamic systems on time scales: Sturmian property of the principal solution. Zbl 1042.34509
Bohner, M.; Došlý, O.; Hilscher, R.
2001
Oscillation theorems for discrete symplectic systems with nonlinear dependence in spectral parameter. Zbl 1258.39005
Šimon Hilscher, Roman
2012
Hamilton-Jacobi theory over time scales and applications to linear-quadratic problems. Zbl 1230.49023
Šimon Hilscher, Roman; Zeidan, Vera
2012
Eigenvalue and oscillation theorems for time scale symplectic systems. Zbl 1218.34039
Kratz, Werner; Šimon Hilscher, Roman; Zeidan, Vera Michel
2011
Genera of conjoined bases of linear Hamiltonian systems and limit characterization of principal solutions at infinity. Zbl 1338.34036
Šepitka, Peter; Šimon Hilscher, Roman
2016
Symplectic difference systems: oscillation and spectral theory. Zbl 1425.39001
Došlý, Ondřej; Elyseeva, Julia; Šimon Hilscher, Roman
2019
Spectral and oscillation theory for general second order Sturm-Liouville difference equations. Zbl 1302.39022
Šimon Hilscher, Roman
2012
Nonnegativity of discrete quadratic functionals corresponding to symplectic difference systems. Zbl 1056.39020
Došlý, Ondřej; Hilscher, Roman; Zeidan, Vera
2003
Linear Hamiltonian systems on time scales: Positivity of quadratic functionals. Zbl 0982.37054
Hilscher, R.
2000
Linear Hamiltonian difference systems: Transformations, recessive solutions, generalized reciprocity. Zbl 0946.39003
Došlý, Ondřej; Hilscher, Roman
1999
Discrete optimal control: The accessory problem and necessary optimality conditions. Zbl 0987.49016
Hilscher, Roman; Zeidan, Vera
2000
Implicit Riccati equations and quadratic functionals for discrete symplectic systems. Zbl 1112.39007
Hilscher, Roman; Růžičková, Viera
2006
An eigenvalue problem for linear Hamiltonian dynamic systems. Zbl 1096.39017
Bohner, Martin; Hilscher, Roman
2005
Weyl-Titchmarsh theory for time scale symplectic systems on half line. Zbl 1217.34144
Šimon Hilscher, Roman; Zemánek, Petr
2011
Symmetric three-term recurrence equations and their symplectic structure. Zbl 1198.39002
Šimon Hilscher, Roman; Zeidan, Vera
2010
First order conditions for generalized variational problems over time scales. Zbl 1236.49061
Šimon Hilscher, Roman; Zeidan, Vera
2011
Limit circle invariance for two differential systems on time scales. Zbl 1312.34142
Šimon Hilscher, Roman; Zemánek, Petr
2015
Focal points and principal solutions of linear Hamiltonian systems revisited. Zbl 1394.34061
Šepitka, Peter; Šimon Hilscher, Roman
2018
Friedrichs extension of operators defined by linear Hamiltonian systems on unbounded interval. Zbl 1220.47028
Šimon Hilscher, Roman; Zemánek, Petr
2010
Coupled intervals in the discrete calculus of variations: necessity and sufficiency. Zbl 1032.49038
Hilscher, Roman; Zeidan, Vera
2002
Oscillation theorems and Rayleigh principle for linear Hamiltonian and symplectic systems with general boundary conditions. Zbl 1257.34077
Šimon Hilscher, Roman; Zeidan, Vera
2012
Multiplicities of focal points for discrete symplectic systems: revisited. Zbl 1188.39005
Hilscher, Roman; Zeidan, Vera
2009
Discrete oscillation theorems for symplectic eigenvalue problems with general boundary conditions depending nonlinearly on spectral parameter. Zbl 1401.39012
Elyseeva, Julia; Šimon Hilscher, Roman
2018
Eigenvalue theory for time scale symplectic systems depending nonlinearly on spectral parameter. Zbl 1309.34148
Šimon Hilscher, Roman
2012
A generalized index theorem for monotone matrix-valued functions with applications to discrete oscillation theory. Zbl 1365.39009
Kratz, W.; Šimon Hilscher, R.
2013
A class of Sturm-Liouville difference equations: (Non)oscillation constants and property BD. Zbl 1054.39013
Došlý, O.; Hilscher, R.
2003
Legendre, Jacobi, and Riccati type conditions for time scale variational problem with application. Zbl 1160.39004
Hilscher, R.; Zeidan, V.
2007
Positivity of quadratic functionals on time scales: Necessity. Zbl 0999.34037
Hilscher, Roman
2001
Oscillation criterion for half-linear differential equations with periodic coefficients. Zbl 1258.34064
Došlý, O.; Özbekler, A.; Šimon Hilscher, R.
2012
Coupled intervals for discrete symplectic systems. Zbl 1115.39019
Hilscher, Roman; Zeidan, Vera
2006
Generalized Lagrange identity for discrete symplectic systems and applications in Weyl-Titchmarsh theory. Zbl 1318.39008
Šimon Hilscher, Roman; Zemánek, Petr
2014
Rayleigh principle for time scale symplectic systems and applications. Zbl 1340.34355
Šimon Hilscher, Roman; Zeidan, Vera
2011
Diagonalization approach to discrete quadratic functionals. Zbl 1033.39003
Bohner, M.; Došlý, O.; Hilscher, R.; Kratz, W.
2003
Reid’s construction of minimal principal solution at infinity for linear Hamiltonian systems. Zbl 1375.37058
Šepitka, Peter; Šimon Hilscher, Roman
2016
Weyl disks and square summable solutions for discrete symplectic systems with jointly varying endpoints. Zbl 1375.39014
Šimon Hilscher, Roman; Zemánek, Petr
2013
Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems. Zbl 1408.37107
Šepitka, Peter; Šimon Hilscher, Roman
2019
Recessive solutions for nonoscillatory discrete symplectic systems. Zbl 1307.39007
Šepitka, Peter; Šimon Hilscher, Roman
2015
Equivalent conditions to the nonnegativity of a quadratic functional in discrete optimal control. Zbl 1042.39007
Hilscher, Roman; Zeidan, Vera
2004
Riccati inequality, disconjugacy, and reciprocity principle for linear Hamiltonian dynamic systems. Zbl 1046.39009
Hilscher, Roman; Řehák, Pavel
2003
Coupled intervals in the discrete optimal control. Zbl 1051.39017
Hilscher, Roman; Zeidan, Vera
2004
Nonnegativity of a discrete quadratic functional in terms of the (strengthened) Legendre and Jacobi conditions. Zbl 1044.49020
Hilscher, R.; Zeidan, V.
2003
Reid roundabout theorems for time scale symplectic systems. Zbl 1229.34138
Hilscher, R.; Zeidan, V.
2010
Picone type identities and definiteness of quadratic functionals on time scales. Zbl 1178.93094
Šimon Hilscher, Roman; Zeidan, Vera
2009
Singular Sturmian comparison theorems for linear Hamiltonian systems. Zbl 1442.37114
Šepitka, Peter; Šimon Hilscher, Roman
2020
A remark on discrete quadratic functionals with separable endpoints. Zbl 1058.39013
Hilscher, Roman; Zeidan, Vera
2003
Linear Hamiltonian systems on time scales: Transformations. Zbl 0997.34005
Hilscher, Roman
1999
Spectral properties of general selfadjoint, even-order differential operators. Zbl 0995.34077
Hilscher, Roman
2000
Nabla time scale symplectic systems and related quadratic functionals. Zbl 1214.34091
Hilscher, Roman; Zeidan, Vera
2010
Trigonometric and hyperbolic systems on time scales. Zbl 1184.34089
Hilscher, R.; Zemánek, P.
2009
Terminal value problems for first and second order nonlinear equations on time scales. Zbl 1176.34059
Hilscher, Roman; Tisdell, Christopher C.
2008
Spectral properties of fourth order differential operators. Zbl 0894.34028
Došlý, O.; Hilscher, R.
1997
Dominant and recessive solutions at infinity and genera of conjoined bases for discrete symplectic systems. Zbl 1376.39004
Šepitka, Peter; Šimon Hilscher, Roman
2017
Time scale symplectic systems with analytic dependence on spectral parameter. Zbl 1312.34141
Šimon Hilscher, Roman; Zemánek, Petr
2015
New results for time reversed symplectic dynamic systems and quadratic functionals. Zbl 1324.34195
Šimon Hilscher, R.; Zemánek, Petr
2012
Sufficiency and sensitivity for nonlinear optimal control problems on time scales via coercivity. Zbl 1415.49015
Šimon Hilscher, Roman; Zeidan, Vera
2018
Sturmian comparison theorems for completely controllable linear Hamiltonian systems in singular case. Zbl 1439.37088
Šepitka, Peter; Šimon Hilscher, Roman
2020
Discrete quadratic functionals with jointly varying endpoints via separable endpoints. Zbl 1065.39033
Hilscher, Roman; Zeidan, Vera
2004
Solvability of the discrete LQR-problem under minimal assumptions. Zbl 1094.39018
Hilscher, Roman; Zeidan, Vera
2005
Asymptotic properties of solutions of Riccati matrix equations and inequalities for discrete symplectic systems. Zbl 1349.39021
Šimon Hilscher, R.
2015
Inhomogeneous quadratic functionals on time scales. Zbl 0974.39008
Hilscher, Roman
2001
Perturbation of nonnegative time scale quadratic functionals. Zbl 1127.39032
Hilscher, R.; Růžičková, V.
2007
Principal solutions at infinity for time scale symplectic systems without controllability condition. Zbl 1343.93057
Šepitka, Peter; Šimon Hilscher, Roman
2016
Comparison theorems for self-adjoint linear Hamiltonian eigenvalue problems. Zbl 1297.34048
Šimon Hilscher, Roman
2014
Eigenvalue comparison for discrete symplectic systems. Zbl 1336.39009
Šimon Hilscher, Roman
2015
On disconjugacy for vector linear Hamiltonian systems on time scales. Zbl 1183.34047
Hilscher, Roman
2000
Comparison results for solutions of time scale matrix Riccati equations and inequalities. Zbl 1171.34313
Hilscher, R.
2006
Singular Sturmian separation theorems for nonoscillatory symplectic difference systems. Zbl 1405.39006
Šepitka, Peter; Šimon Hilscher, Roman
2018
Distribution and number of focal points for linear Hamiltonian systems. Zbl 1460.37082
Šepitka, Peter; Šimon Hilscher, Roman
2021
Lidskii angles and Sturmian theory for linear Hamiltonian systems on compact interval. Zbl 1478.37057
Šepitka, Peter; Šimon Hilscher, Roman
2021
Distribution and number of focal points for linear Hamiltonian systems. Zbl 1460.37082
Šepitka, Peter; Šimon Hilscher, Roman
2021
Lidskii angles and Sturmian theory for linear Hamiltonian systems on compact interval. Zbl 1478.37057
Šepitka, Peter; Šimon Hilscher, Roman
2021
Singular Sturmian comparison theorems for linear Hamiltonian systems. Zbl 1442.37114
Šepitka, Peter; Šimon Hilscher, Roman
2020
Sturmian comparison theorems for completely controllable linear Hamiltonian systems in singular case. Zbl 1439.37088
Šepitka, Peter; Šimon Hilscher, Roman
2020
Symplectic difference systems: oscillation and spectral theory. Zbl 1425.39001
Došlý, Ondřej; Elyseeva, Julia; Šimon Hilscher, Roman
2019
Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems. Zbl 1408.37107
Šepitka, Peter; Šimon Hilscher, Roman
2019
Focal points and principal solutions of linear Hamiltonian systems revisited. Zbl 1394.34061
Šepitka, Peter; Šimon Hilscher, Roman
2018
Discrete oscillation theorems for symplectic eigenvalue problems with general boundary conditions depending nonlinearly on spectral parameter. Zbl 1401.39012
Elyseeva, Julia; Šimon Hilscher, Roman
2018
Sufficiency and sensitivity for nonlinear optimal control problems on time scales via coercivity. Zbl 1415.49015
Šimon Hilscher, Roman; Zeidan, Vera
2018
Singular Sturmian separation theorems for nonoscillatory symplectic difference systems. Zbl 1405.39006
Šepitka, Peter; Šimon Hilscher, Roman
2018
Comparative index and Sturmian theory for linear Hamiltonian systems. Zbl 1375.34052
Šepitka, Peter; Šimon Hilscher, Roman
2017
Dominant and recessive solutions at infinity and genera of conjoined bases for discrete symplectic systems. Zbl 1376.39004
Šepitka, Peter; Šimon Hilscher, Roman
2017
Genera of conjoined bases of linear Hamiltonian systems and limit characterization of principal solutions at infinity. Zbl 1338.34036
Šepitka, Peter; Šimon Hilscher, Roman
2016
Reid’s construction of minimal principal solution at infinity for linear Hamiltonian systems. Zbl 1375.37058
Šepitka, Peter; Šimon Hilscher, Roman
2016
Principal solutions at infinity for time scale symplectic systems without controllability condition. Zbl 1343.93057
Šepitka, Peter; Šimon Hilscher, Roman
2016
Principal solutions at infinity of given ranks for nonoscillatory linear Hamiltonian systems. Zbl 1348.37091
Šepitka, Peter; Šimon Hilscher, Roman
2015
Principal and antiprincipal solutions at infinity of linear Hamiltonian systems. Zbl 1329.34024
Šepitka, Peter; Šimon Hilscher, Roman
2015
Limit circle invariance for two differential systems on time scales. Zbl 1312.34142
Šimon Hilscher, Roman; Zemánek, Petr
2015
Recessive solutions for nonoscillatory discrete symplectic systems. Zbl 1307.39007
Šepitka, Peter; Šimon Hilscher, Roman
2015
Time scale symplectic systems with analytic dependence on spectral parameter. Zbl 1312.34141
Šimon Hilscher, Roman; Zemánek, Petr
2015
Asymptotic properties of solutions of Riccati matrix equations and inequalities for discrete symplectic systems. Zbl 1349.39021
Šimon Hilscher, R.
2015
Eigenvalue comparison for discrete symplectic systems. Zbl 1336.39009
Šimon Hilscher, Roman
2015
Minimal principal solution at infinity for nonoscillatory linear Hamiltonian systems. Zbl 1305.34053
Šepitka, Peter; Šimon Hilscher, Roman
2014
Weyl-Titchmarsh theory for discrete symplectic systems with general linear dependence on spectral parameter. Zbl 1312.39011
Šimon Hilscher, Roman; Zemánek, Petr
2014
Limit point and limit circle classification for symplectic systems on time scales. Zbl 1334.34197
Šimon Hilscher, Roman; Zemánek, Petr
2014
Generalized Lagrange identity for discrete symplectic systems and applications in Weyl-Titchmarsh theory. Zbl 1318.39008
Šimon Hilscher, Roman; Zemánek, Petr
2014
Comparison theorems for self-adjoint linear Hamiltonian eigenvalue problems. Zbl 1297.34048
Šimon Hilscher, Roman
2014
A generalized index theorem for monotone matrix-valued functions with applications to discrete oscillation theory. Zbl 1365.39009
Kratz, W.; Šimon Hilscher, R.
2013
Weyl disks and square summable solutions for discrete symplectic systems with jointly varying endpoints. Zbl 1375.39014
Šimon Hilscher, Roman; Zemánek, Petr
2013
Rayleigh principle for linear Hamiltonian systems without controllability. Zbl 1254.34120
Kratz, Werner; Šimon Hilscher, Roman
2012
Oscillation and spectral theory for linear Hamiltonian systems with nonlinear dependence on the spectral parameter. Zbl 1254.34119
Bohner, Martin; Kratz, Werner; Šimon Hilscher, Roman
2012
Oscillation theorems for discrete symplectic systems with nonlinear dependence in spectral parameter. Zbl 1258.39005
Šimon Hilscher, Roman
2012
Hamilton-Jacobi theory over time scales and applications to linear-quadratic problems. Zbl 1230.49023
Šimon Hilscher, Roman; Zeidan, Vera
2012
Spectral and oscillation theory for general second order Sturm-Liouville difference equations. Zbl 1302.39022
Šimon Hilscher, Roman
2012
Oscillation theorems and Rayleigh principle for linear Hamiltonian and symplectic systems with general boundary conditions. Zbl 1257.34077
Šimon Hilscher, Roman; Zeidan, Vera
2012
Eigenvalue theory for time scale symplectic systems depending nonlinearly on spectral parameter. Zbl 1309.34148
Šimon Hilscher, Roman
2012
Oscillation criterion for half-linear differential equations with periodic coefficients. Zbl 1258.34064
Došlý, O.; Özbekler, A.; Šimon Hilscher, R.
2012
New results for time reversed symplectic dynamic systems and quadratic functionals. Zbl 1324.34195
Šimon Hilscher, R.; Zemánek, Petr
2012
Sturmian theory for linear Hamiltonian systems without controllability. Zbl 1218.34038
Šimon Hilscher, Roman
2011
On general Sturmian theory for abnormal linear Hamiltonian systems. Zbl 1306.34051
Šimon Hilscher, Roman
2011
Eigenvalue and oscillation theorems for time scale symplectic systems. Zbl 1218.34039
Kratz, Werner; Šimon Hilscher, Roman; Zeidan, Vera Michel
2011
Weyl-Titchmarsh theory for time scale symplectic systems on half line. Zbl 1217.34144
Šimon Hilscher, Roman; Zemánek, Petr
2011
First order conditions for generalized variational problems over time scales. Zbl 1236.49061
Šimon Hilscher, Roman; Zeidan, Vera
2011
Rayleigh principle for time scale symplectic systems and applications. Zbl 1340.34355
Šimon Hilscher, Roman; Zeidan, Vera
2011
Symmetric three-term recurrence equations and their symplectic structure. Zbl 1198.39002
Šimon Hilscher, Roman; Zeidan, Vera
2010
Friedrichs extension of operators defined by linear Hamiltonian systems on unbounded interval. Zbl 1220.47028
Šimon Hilscher, Roman; Zemánek, Petr
2010
Reid roundabout theorems for time scale symplectic systems. Zbl 1229.34138
Hilscher, R.; Zeidan, V.
2010
Nabla time scale symplectic systems and related quadratic functionals. Zbl 1214.34091
Hilscher, Roman; Zeidan, Vera
2010
Weak maximum principle and accessory problem for control problems on time scales. Zbl 1157.49030
Hilscher, Roman; Zeidan, Vera
2009
Multiplicities of focal points for discrete symplectic systems: revisited. Zbl 1188.39005
Hilscher, Roman; Zeidan, Vera
2009
Picone type identities and definiteness of quadratic functionals on time scales. Zbl 1178.93094
Šimon Hilscher, Roman; Zeidan, Vera
2009
Trigonometric and hyperbolic systems on time scales. Zbl 1184.34089
Hilscher, R.; Zemánek, P.
2009
Applications of time scale symplectic systems without normality. Zbl 1145.39006
Hilscher, Roman; Zeidan, Vera
2008
Riccati equations for abnormal time scale quadratic functionals. Zbl 1355.49031
Hilscher, Roman; Zeidan, Vera
2008
Time scale embedding theorem and coercivity of quadratic functionals. Zbl 1136.49017
Hilscher, Roman; Zeidan, Vera
2008
Terminal value problems for first and second order nonlinear equations on time scales. Zbl 1176.34059
Hilscher, Roman; Tisdell, Christopher C.
2008
Legendre, Jacobi, and Riccati type conditions for time scale variational problem with application. Zbl 1160.39004
Hilscher, R.; Zeidan, V.
2007
Perturbation of nonnegative time scale quadratic functionals. Zbl 1127.39032
Hilscher, R.; Růžičková, V.
2007
Riccati inequality and other results for discrete symplectic systems. Zbl 1103.39020
Hilscher, Roman; Růžičková, Viera
2006
Time scale symplectic systems without normality. Zbl 1104.37037
Hilscher, Roman; Zeidan, Vera
2006
Implicit Riccati equations and quadratic functionals for discrete symplectic systems. Zbl 1112.39007
Hilscher, Roman; Růžičková, Viera
2006
Coupled intervals for discrete symplectic systems. Zbl 1115.39019
Hilscher, Roman; Zeidan, Vera
2006
Comparison results for solutions of time scale matrix Riccati equations and inequalities. Zbl 1171.34313
Hilscher, R.
2006
Nonnegativity and positivity of quadratic functionals in discrete calculus of variations: survey. Zbl 1098.49025
Hilscher, Roman; Zeidan, Vera
2005
An eigenvalue problem for linear Hamiltonian dynamic systems. Zbl 1096.39017
Bohner, Martin; Hilscher, Roman
2005
Solvability of the discrete LQR-problem under minimal assumptions. Zbl 1094.39018
Hilscher, Roman; Zeidan, Vera
2005
Calculus of variations on time scales: Weak local piecewise $$C_{\text{rd}}^{1}$$ solutions with variable endpoints. Zbl 1043.49004
Hilscher, Roman; Zeidan, Vera
2004
Equivalent conditions to the nonnegativity of a quadratic functional in discrete optimal control. Zbl 1042.39007
Hilscher, Roman; Zeidan, Vera
2004
Coupled intervals in the discrete optimal control. Zbl 1051.39017
Hilscher, Roman; Zeidan, Vera
2004
Discrete quadratic functionals with jointly varying endpoints via separable endpoints. Zbl 1065.39033
Hilscher, Roman; Zeidan, Vera
2004
Symplectic difference systems: Variable stepsize discretization and discrete quadratic functionals. Zbl 1021.39008
Hilscher, Roman; Zeidan, Vera
2003
Nonnegativity of discrete quadratic functionals corresponding to symplectic difference systems. Zbl 1056.39020
Došlý, Ondřej; Hilscher, Roman; Zeidan, Vera
2003
A class of Sturm-Liouville difference equations: (Non)oscillation constants and property BD. Zbl 1054.39013
Došlý, O.; Hilscher, R.
2003
Diagonalization approach to discrete quadratic functionals. Zbl 1033.39003
Bohner, M.; Došlý, O.; Hilscher, R.; Kratz, W.
2003
Riccati inequality, disconjugacy, and reciprocity principle for linear Hamiltonian dynamic systems. Zbl 1046.39009
Hilscher, Roman; Řehák, Pavel
2003
Nonnegativity of a discrete quadratic functional in terms of the (strengthened) Legendre and Jacobi conditions. Zbl 1044.49020
Hilscher, R.; Zeidan, V.
2003
A remark on discrete quadratic functionals with separable endpoints. Zbl 1058.39013
Hilscher, Roman; Zeidan, Vera
2003
Second order sufficiency criteria for a discrete optimal control problem. Zbl 1010.49020
Hilscher, Roman; Zeidan, Vera
2002
A time scales version of a Wirtinger-type inequality and applications. Zbl 1025.26012
Hilscher, Roman
2002
Discrete optimal control: Second order optimality conditions. Zbl 1010.49021
Hilscher, Roman; Zeidan, Vera
2002
Coupled intervals in the discrete calculus of variations: necessity and sufficiency. Zbl 1032.49038
Hilscher, Roman; Zeidan, Vera
2002
Disconjugacy, transformations and quadratic functionals for symplectic dynamic systems on time scales. Zbl 0989.34027
Došlý, Ondřej; Hilscher, Roman
2001
Reid roundabout theorem for symplectic dynamic systems on time scales. Zbl 0990.39017
Hilscher, R.
2001
Discrete spectra criteria for certain classes of singular differential and difference operators. Zbl 1008.39011
Hilscher, R.
2001
Linear Hamiltonian dynamic systems on time scales: Sturmian property of the principal solution. Zbl 1042.34509
Bohner, M.; Došlý, O.; Hilscher, R.
2001
Positivity of quadratic functionals on time scales: Necessity. Zbl 0999.34037
Hilscher, Roman
2001
Inhomogeneous quadratic functionals on time scales. Zbl 0974.39008
Hilscher, Roman
2001
Linear Hamiltonian systems on time scales: Positivity of quadratic functionals. Zbl 0982.37054
Hilscher, R.
2000
Discrete optimal control: The accessory problem and necessary optimality conditions. Zbl 0987.49016
Hilscher, Roman; Zeidan, Vera
2000
Spectral properties of general selfadjoint, even-order differential operators. Zbl 0995.34077
Hilscher, Roman
2000
On disconjugacy for vector linear Hamiltonian systems on time scales. Zbl 1183.34047
Hilscher, Roman
2000
Disconjugacy of symplectic systems and positive definiteness of block tridiagonal matrices. Zbl 0956.39010
Hilscher, Roman
1999
Linear Hamiltonian difference systems: Transformations, recessive solutions, generalized reciprocity. Zbl 0946.39003
Došlý, Ondřej; Hilscher, Roman
1999
Linear Hamiltonian systems on time scales: Transformations. Zbl 0997.34005
Hilscher, Roman
1999
Spectral properties of fourth order differential operators. Zbl 0894.34028
Došlý, O.; Hilscher, R.
1997
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### Cited by 271 Authors

 64 Šimon Hilscher, Roman 24 Zeidan, Vera Michel 19 Šepitka, Peter 18 Došlý, Ondřej 17 Zemánek, Petr 14 Elyseeva, Julia V. 11 Bohner, Martin J. 9 Eldeeb, Ahmed Abdel-Moneim 8 Kratz, Werner 8 Marinković, Boban 6 Shi, Yuming 5 Bartosiewicz, Zbigniew 5 Mardanov, Misir Dzhumail ogly 5 Nguyen Thi Toan 5 Ren, Guojing 5 Sugie, Jitsuro 5 Torres, Delfim Fernando Marado 4 Clark, Stephen L. 4 Liu, Wenjun J. 4 Malik, Samin T. 4 Malinowska, Agnieszka Barbara 4 Martins, Natália F. 4 Ngô Quốc Anh 4 Núñez Jiménez, Carmen 4 Song, Chuanjing 4 Sun, Huaqing 4 Thuy, Le Quang 4 Zhang, Yi 3 Bourdin, Loïc 3 Elsennary, Hamza A. 3 Gao, Chenghua 3 Gavrikov, Alexander A. 3 Jia, Guangyan 3 Khan, Zareen Abdulhameed 3 Lv, Weidong 3 Melikov, Telman Kuli 3 Obaya, Rafael 3 Řehák, Pavel 3 Sakhnovich, Alexander L. 3 Ugurlu, Ekin 3 Wei, Wei 3 Zhan, Zaidong 3 Zhou, Zhan 3 Zhu, Yingjun 2 Agarwal, Ravi P. 2 Ahlbrandt, Calvin D. 2 Akulenko, Leonid Denisovich 2 Anderson, Douglas Robert 2 dos Santos, Iguer Luis Domini 2 Dřímalová, Iva 2 Fabbri, Roberta 2 Ferreira, Rui A. C. 2 Grow, David E. 2 Guseinov, Gusein Sh. 2 Hasil, Petr 2 Heidarkhani, Shapour 2 Hilger, Stefan 2 Ishibashi, Kazuki 2 Jiang, Liqun 2 Kong, Qingkai 2 Kotta, Ulle 2 Mahmudov, Elimhan Nadir 2 Mahmudov, Nazim Idrisoglu 2 Merdivenci Atici, Ferhan 2 Nesterov, Sergeĭ V. 2 Novo, Sylvia 2 Nwaeze, Eze Raymond 2 Ozkan, Ahmet Sinan 2 Pawłuszewicz, Ewa 2 Peng, Yunfei 2 Saker, Samir H. 2 Sun, Shurong 2 Trélat, Emmanuel 2 Wintz, Nick 2 Wyrwas, Małgorzata 2 Xiang, Xiaoling 2 Yamaoka, Naoto 2 Zhang, Chao 2 Zhang, Fei 2 Zheng, Zhaowen 1 Abdo, Khadega R. 1 Abutaleb, Ahmad Adel 1 Acharya, Keshav Raj 1 Adalar, Ibrahim 1 Adivar, Murat 1 Agarwal, Praveen 1 Ahmed, Elsayed 1 Akin, Elvan 1 Aliyev, Ziyatkhan S. 1 Almeida, Ricardo 1 Alomari, Mohammad Wajeeh 1 An, D. T. V. 1 Anerot, Baptiste 1 Ansari, Qamrul Hasan 1 Ayazi, Farahnaz 1 Aydin, Muhittin Evren 1 Bai, Jie 1 Bai, Ling 1 Bairamov, Elgiz 1 Bajaj, Chanderjit L. ...and 171 more Authors
all top 5

### Cited in 102 Serials

 26 Journal of Mathematical Analysis and Applications 22 Advances in Difference Equations 20 Applied Mathematics and Computation 19 Journal of Difference Equations and Applications 13 Linear Algebra and its Applications 12 Journal of Differential Equations 11 Computers & Mathematics with Applications 11 Applied Mathematics Letters 7 Journal of Computational and Applied Mathematics 7 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 5 Mathematische Nachrichten 5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 Journal of Dynamics and Differential Equations 5 Abstract and Applied Analysis 4 Journal of Mathematical Physics 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 Discrete Dynamics in Nature and Society 4 Boundary Value Problems 3 Rocky Mountain Journal of Mathematics 3 Journal of Optimization Theory and Applications 3 Positivity 3 Differential Equations 2 Mathematica Slovaca 2 Monatshefte für Mathematik 2 Numerical Functional Analysis and Optimization 2 Quaestiones Mathematicae 2 Mathematical and Computer Modelling 2 Filomat 2 Complexity 2 Journal of Inequalities and Applications 2 Nonlinear Analysis. Hybrid Systems 1 International Journal of Control 1 International Journal of Theoretical Physics 1 Inverse Problems 1 Journal of the Franklin Institute 1 Linear and Multilinear Algebra 1 Mathematical Notes 1 Moscow University Mechanics Bulletin 1 Reports on Mathematical Physics 1 Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 1 Applied Mathematics and Optimization 1 Automatica 1 Dissertationes Mathematicae 1 Fasciculi Mathematici 1 International Journal of Mathematics and Mathematical Sciences 1 Integral Equations and Operator Theory 1 Meccanica 1 Results in Mathematics 1 Transactions of the American Mathematical Society 1 Systems & Control Letters 1 Acta Applicandae Mathematicae 1 Physica D 1 Optimization 1 Discrete & Computational Geometry 1 Signal Processing 1 IMRN. International Mathematics Research Notices 1 The Journal of Geometric Analysis 1 Journal of Global Optimization 1 Computational Mathematics and Mathematical Physics 1 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 1 Archives of Control Sciences 1 Journal of Mathematical Sciences (New York) 1 Computational and Applied Mathematics 1 Journal of Inverse and Ill-Posed Problems 1 Opuscula Mathematica 1 Discrete and Continuous Dynamical Systems 1 Documenta Mathematica 1 Mathematical Problems in Engineering 1 European Journal of Control 1 Differential Equations and Dynamical Systems 1 Optimization Methods & Software 1 Taiwanese Journal of Mathematics 1 Mathematical Methods of Operations Research 1 Analysis (München) 1 Journal of Dynamical and Control Systems 1 The ANZIAM Journal 1 Nonlinear Analysis. Modelling and Control 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Communications on Pure and Applied Analysis 1 Computational Methods and Function Theory 1 Journal of Dynamical Systems and Geometric Theories 1 Hacettepe Journal of Mathematics and Statistics 1 Mediterranean Journal of Mathematics 1 Journal of Industrial and Management Optimization 1 Communications in Mathematical Analysis 1 Complex Analysis and Operator Theory 1 Optimization Letters 1 Operators and Matrices 1 Journal of Mathematical Inequalities 1 Discrete and Continuous Dynamical Systems. Series S 1 Journal of Nonlinear Science and Applications 1 Differential Equations and Applications 1 Advances in Mathematical Physics 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Annals of Functional Analysis 1 Analysis and Mathematical Physics 1 Mathematical Control and Related Fields 1 Journal of Applied Analysis and Computation 1 Journal of Function Spaces 1 AIMS Mathematics ...and 2 more Serials
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### Cited in 33 Fields

 147 Ordinary differential equations (34-XX) 117 Difference and functional equations (39-XX) 69 Calculus of variations and optimal control; optimization (49-XX) 66 Dynamical systems and ergodic theory (37-XX) 45 Systems theory; control (93-XX) 35 Real functions (26-XX) 23 Operations research, mathematical programming (90-XX) 18 Operator theory (47-XX) 14 Linear and multilinear algebra; matrix theory (15-XX) 14 Mechanics of particles and systems (70-XX) 9 Partial differential equations (35-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Numerical analysis (65-XX) 4 Mechanics of deformable solids (74-XX) 4 Quantum theory (81-XX) 3 Integral equations (45-XX) 2 Functional analysis (46-XX) 2 Differential geometry (53-XX) 2 Probability theory and stochastic processes (60-XX) 2 Computer science (68-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Biology and other natural sciences (92-XX) 1 Combinatorics (05-XX) 1 Algebraic geometry (14-XX) 1 Topological groups, Lie groups (22-XX) 1 Functions of a complex variable (30-XX) 1 Approximations and expansions (41-XX) 1 Integral transforms, operational calculus (44-XX) 1 Statistics (62-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Geophysics (86-XX) 1 Information and communication theory, circuits (94-XX)