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Šimon Hilscher, Roman

Author ID: simon-hilscher.roman Recent zbMATH articles by "Šimon Hilscher, Roman"
Published as: Šimon Hilscher, Roman; Hilscher, Roman; Hilscher, R.; Šimon Hilscher, R.; Hilscher, Roman Šimon
Homepage: https://www.math.muni.cz/~hilscher/
External Links: MGP · ORCID · dblp
Documents Indexed: 108 Publications since 1997, including 2 Books
3 Contributions as Editor
Reviewing Activity: 172 Reviews
Co-Authors: 17 Co-Authors with 90 Joint Publications
642 Co-Co-Authors
all top 5

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 Archivum Mathematicum
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 Journal of Dynamics and Differential Equations
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 Discrete and Continuous Dynamical Systems
1 Applied Mathematics and Optimization
1 Fasciculi Mathematici
1 Journal of Computational and Applied Mathematics
1 Mathematica Slovaca
1 Monatshefte für Mathematik
1 Mathematical and Computer Modelling
1 SIAM Journal on Matrix Analysis and Applications
1 Electronic Journal of Differential Equations (EJDE)
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

Publications by Year

Citations contained in zbMATH Open

101 Publications have been cited 991 times in 312 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
47
2004
Weak maximum principle and accessory problem for control problems on time scales. Zbl 1157.49030
Hilscher, Roman; Zeidan, Vera
35
2009
Disconjugacy, transformations and quadratic functionals for symplectic dynamic systems on time scales. Zbl 0989.34027
Došlý, Ondřej; Hilscher, Roman
28
2001
Minimal principal solution at infinity for nonoscillatory linear Hamiltonian systems. Zbl 1305.34053
Šepitka, Peter; Šimon Hilscher, Roman
28
2014
Sturmian theory for linear Hamiltonian systems without controllability. Zbl 1218.34038
Šimon Hilscher, Roman
27
2011
Second order sufficiency criteria for a discrete optimal control problem. Zbl 1010.49020
Hilscher, Roman; Zeidan, Vera
24
2002
Reid roundabout theorem for symplectic dynamic systems on time scales. Zbl 0990.39017
Hilscher, R.
23
2001
Symplectic difference systems: Variable stepsize discretization and discrete quadratic functionals. Zbl 1021.39008
Hilscher, Roman; Zeidan, Vera
22
2003
Comparative index and Sturmian theory for linear Hamiltonian systems. Zbl 1375.34052
Šepitka, Peter; Šimon Hilscher, Roman
22
2017
Rayleigh principle for linear Hamiltonian systems without controllability. Zbl 1254.34120
Kratz, Werner; Šimon Hilscher, Roman
22
2012
On general Sturmian theory for abnormal linear Hamiltonian systems. Zbl 1306.34051
Šimon Hilscher, Roman
22
2011
Discrete optimal control: Second order optimality conditions. Zbl 1010.49021
Hilscher, Roman; Zeidan, Vera
21
2002
A time scales version of a Wirtinger-type inequality and applications. Zbl 1025.26012
Hilscher, Roman
21
2002
Principal solutions at infinity of given ranks for nonoscillatory linear Hamiltonian systems. Zbl 1348.37091
Šepitka, Peter; Šimon Hilscher, Roman
20
2015
Weyl-Titchmarsh theory for discrete symplectic systems with general linear dependence on spectral parameter. Zbl 1312.39011
Šimon Hilscher, Roman; Zemánek, Petr
19
2014
Symplectic difference systems: oscillation and spectral theory. Zbl 1425.39001
Došlý, Ondřej; Elyseeva, Julia; Šimon Hilscher, Roman
19
2019
Applications of time scale symplectic systems without normality. Zbl 1145.39006
Hilscher, Roman; Zeidan, Vera
18
2008
Limit point and limit circle classification for symplectic systems on time scales. Zbl 1334.34197
Šimon Hilscher, Roman; Zemánek, Petr
18
2014
Riccati equations for abnormal time scale quadratic functionals. Zbl 1355.49031
Hilscher, Roman; Zeidan, Vera
17
2008
Principal and antiprincipal solutions at infinity of linear Hamiltonian systems. Zbl 1329.34024
Šepitka, Peter; Šimon Hilscher, Roman
16
2015
Nonnegativity and positivity of quadratic functionals in discrete calculus of variations: survey. Zbl 1098.49025
Hilscher, Roman; Zeidan, Vera
15
2005
Time scale embedding theorem and coercivity of quadratic functionals. Zbl 1136.49017
Hilscher, Roman; Zeidan, Vera
15
2008
Riccati inequality and other results for discrete symplectic systems. Zbl 1103.39020
Hilscher, Roman; Růžičková, Viera
14
2006
Time scale symplectic systems without normality. Zbl 1104.37037
Hilscher, Roman; Zeidan, Vera
14
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
14
2012
Eigenvalue and oscillation theorems for time scale symplectic systems. Zbl 1218.34039
Kratz, Werner; Šimon Hilscher, Roman; Zeidan, Vera Michel
13
2011
Hamilton-Jacobi theory over time scales and applications to linear-quadratic problems. Zbl 1230.49023
Šimon Hilscher, Roman; Zeidan, Vera
13
2012
Spectral and oscillation theory for general second order Sturm-Liouville difference equations. Zbl 1302.39022
Šimon Hilscher, Roman
13
2012
Linear Hamiltonian dynamic systems on time scales: Sturmian property of the principal solution. Zbl 1042.34509
Bohner, M.; Došlý, O.; Hilscher, R.
13
2001
Discrete spectra criteria for certain classes of singular differential and difference operators. Zbl 1008.39011
Hilscher, R.
12
2001
Disconjugacy of symplectic systems and positive definiteness of block tridiagonal matrices. Zbl 0956.39010
Hilscher, Roman
12
1999
Genera of conjoined bases of linear Hamiltonian systems and limit characterization of principal solutions at infinity. Zbl 1338.34036
Šepitka, Peter; Šimon Hilscher, Roman
12
2016
Oscillation theorems for discrete symplectic systems with nonlinear dependence in spectral parameter. Zbl 1258.39005
Šimon Hilscher, Roman
12
2012
Linear Hamiltonian systems on time scales: Positivity of quadratic functionals. Zbl 0982.37054
Hilscher, R.
11
2000
Implicit Riccati equations and quadratic functionals for discrete symplectic systems. Zbl 1112.39007
Hilscher, Roman; Růžičková, Viera
11
2006
Weyl-Titchmarsh theory for time scale symplectic systems on half line. Zbl 1217.34144
Šimon Hilscher, Roman; Zemánek, Petr
11
2011
Limit circle invariance for two differential systems on time scales. Zbl 1312.34142
Šimon Hilscher, Roman; Zemánek, Petr
11
2015
Discrete optimal control: The accessory problem and necessary optimality conditions. Zbl 0987.49016
Hilscher, Roman; Zeidan, Vera
10
2000
Focal points and principal solutions of linear Hamiltonian systems revisited. Zbl 1394.34061
Šepitka, Peter; Šimon Hilscher, Roman
10
2018
Friedrichs extension of operators defined by linear Hamiltonian systems on unbounded interval. Zbl 1220.47028
Šimon Hilscher, Roman; Zemánek, Petr
9
2010
Nonnegativity of discrete quadratic functionals corresponding to symplectic difference systems. Zbl 1056.39020
Došlý, Ondřej; Hilscher, Roman; Zeidan, Vera
9
2003
Linear Hamiltonian difference systems: Transformations, recessive solutions, generalized reciprocity. Zbl 0946.39003
Došlý, Ondřej; Hilscher, Roman
9
1999
Discrete oscillation theorems for symplectic eigenvalue problems with general boundary conditions depending nonlinearly on spectral parameter. Zbl 1401.39012
Elyseeva, Julia; Šimon Hilscher, Roman
9
2018
Symmetric three-term recurrence equations and their symplectic structure. Zbl 1198.39002
Šimon Hilscher, Roman; Zeidan, Vera
8
2010
First order conditions for generalized variational problems over time scales. Zbl 1236.49061
Šimon Hilscher, Roman; Zeidan, Vera
8
2011
A generalized index theorem for monotone matrix-valued functions with applications to discrete oscillation theory. Zbl 1365.39009
Kratz, W.; Šimon Hilscher, R.
8
2013
An eigenvalue problem for linear Hamiltonian dynamic systems. Zbl 1096.39017
Bohner, Martin; Hilscher, Roman
8
2005
Singular Sturmian comparison theorems for linear Hamiltonian systems. Zbl 1442.37114
Šepitka, Peter; Šimon Hilscher, Roman
8
2020
Reid’s construction of minimal principal solution at infinity for linear Hamiltonian systems. Zbl 1375.37058
Šepitka, Peter; Šimon Hilscher, Roman
8
2016
Rayleigh principle for time scale symplectic systems and applications. Zbl 1340.34355
Šimon Hilscher, Roman; Zeidan, Vera
8
2011
Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems. Zbl 1408.37107
Šepitka, Peter; Šimon Hilscher, Roman
8
2019
Coupled intervals in the discrete calculus of variations: necessity and sufficiency. Zbl 1032.49038
Hilscher, Roman; Zeidan, Vera
7
2002
Multiplicities of focal points for discrete symplectic systems: revisited. Zbl 1188.39005
Hilscher, Roman; Zeidan, Vera
7
2009
Eigenvalue theory for time scale symplectic systems depending nonlinearly on spectral parameter. Zbl 1309.34148
Šimon Hilscher, Roman
7
2012
A class of Sturm-Liouville difference equations: (Non)oscillation constants and property BD. Zbl 1054.39013
Došlý, O.; Hilscher, R.
7
2003
Oscillation theorems and Rayleigh principle for linear Hamiltonian and symplectic systems with general boundary conditions. Zbl 1257.34077
Šimon Hilscher, Roman; Zeidan, Vera
7
2012
Oscillation criterion for half-linear differential equations with periodic coefficients. Zbl 1258.34064
Došlý, O.; Özbekler, A.; Šimon Hilscher, R.
7
2012
Positivity of quadratic functionals on time scales: Necessity. Zbl 0999.34037
Hilscher, Roman
6
2001
Coupled intervals for discrete symplectic systems. Zbl 1115.39019
Hilscher, Roman; Zeidan, Vera
6
2006
Generalized Lagrange identity for discrete symplectic systems and applications in Weyl-Titchmarsh theory. Zbl 1318.39008
Šimon Hilscher, Roman; Zemánek, Petr
6
2014
Weyl disks and square summable solutions for discrete symplectic systems with jointly varying endpoints. Zbl 1375.39014
Šimon Hilscher, Roman; Zemánek, Petr
6
2013
Legendre, Jacobi, and Riccati type conditions for time scale variational problem with application. Zbl 1160.39004
Hilscher, R.; Zeidan, V.
6
2007
Diagonalization approach to discrete quadratic functionals. Zbl 1033.39003
Bohner, M.; Došlý, O.; Hilscher, R.; Kratz, W.
5
2003
Time scale symplectic systems with analytic dependence on spectral parameter. Zbl 1312.34141
Šimon Hilscher, Roman; Zemánek, Petr
5
2015
Recessive solutions for nonoscillatory discrete symplectic systems. Zbl 1307.39007
Šepitka, Peter; Šimon Hilscher, Roman
5
2015
Dominant and recessive solutions at infinity and genera of conjoined bases for discrete symplectic systems. Zbl 1376.39004
Šepitka, Peter; Šimon Hilscher, Roman
5
2017
Picone type identities and definiteness of quadratic functionals on time scales. Zbl 1178.93094
Šimon Hilscher, Roman; Zeidan, Vera
4
2009
Reid roundabout theorems for time scale symplectic systems. Zbl 1229.34138
Hilscher, R.; Zeidan, V.
4
2010
Equivalent conditions to the nonnegativity of a quadratic functional in discrete optimal control. Zbl 1042.39007
Hilscher, Roman; Zeidan, Vera
4
2004
Nonnegativity of a discrete quadratic functional in terms of the (strengthened) Legendre and Jacobi conditions. Zbl 1044.49020
Hilscher, R.; Zeidan, V.
4
2003
Principal solutions at infinity for time scale symplectic systems without controllability condition. Zbl 1343.93057
Šepitka, Peter; Šimon Hilscher, Roman
4
2016
New results for time reversed symplectic dynamic systems and quadratic functionals. Zbl 1324.34195
Šimon Hilscher, R.; Zemánek, Petr
4
2012
Distribution and number of focal points for linear Hamiltonian systems. Zbl 1460.37082
Šepitka, Peter; Šimon Hilscher, Roman
4
2021
Riccati inequality, disconjugacy, and reciprocity principle for linear Hamiltonian dynamic systems. Zbl 1046.39009
Hilscher, Roman; Řehák, Pavel
4
2003
Coupled intervals in the discrete optimal control. Zbl 1051.39017
Hilscher, Roman; Zeidan, Vera
4
2004
Sufficiency and sensitivity for nonlinear optimal control problems on time scales via coercivity. Zbl 1415.49015
Šimon Hilscher, Roman; Zeidan, Vera
4
2018
Singular Sturmian separation theorems for nonoscillatory symplectic difference systems. Zbl 1405.39006
Šepitka, Peter; Šimon Hilscher, Roman
4
2018
Spectral properties of fourth order differential operators. Zbl 0894.34028
Došlý, O.; Hilscher, R.
3
1997
Terminal value problems for first and second order nonlinear equations on time scales. Zbl 1176.34059
Hilscher, Roman; Tisdell, Christopher C.
3
2008
Nabla time scale symplectic systems and related quadratic functionals. Zbl 1214.34091
Hilscher, Roman; Zeidan, Vera
3
2010
A remark on discrete quadratic functionals with separable endpoints. Zbl 1058.39013
Hilscher, Roman; Zeidan, Vera
3
2003
Sturmian comparison theorems for completely controllable linear Hamiltonian systems in singular case. Zbl 1439.37088
Šepitka, Peter; Šimon Hilscher, Roman
3
2020
Spectral properties of general selfadjoint, even-order differential operators. Zbl 0995.34077
Hilscher, Roman
3
2000
Linear Hamiltonian systems on time scales: Transformations. Zbl 0997.34005
Hilscher, Roman
3
1999
Trigonometric and hyperbolic systems on time scales. Zbl 1184.34089
Hilscher, R.; Zemánek, P.
3
2009
Discrete quadratic functionals with jointly varying endpoints via separable endpoints. Zbl 1065.39033
Hilscher, Roman; Zeidan, Vera
2
2004
Inhomogeneous quadratic functionals on time scales. Zbl 0974.39008
Hilscher, Roman
2
2001
Perturbation of nonnegative time scale quadratic functionals. Zbl 1127.39032
Hilscher, R.; Růžičková, V.
2
2007
Solvability of the discrete LQR-problem under minimal assumptions. Zbl 1094.39018
Hilscher, Roman; Zeidan, Vera
2
2005
Asymptotic properties of solutions of Riccati matrix equations and inequalities for discrete symplectic systems. Zbl 1349.39021
Šimon Hilscher, R.
2
2015
Lidskii angles and Sturmian theory for linear Hamiltonian systems on compact interval. Zbl 1478.37057
Šepitka, Peter; Šimon Hilscher, Roman
2
2021
Antiprincipal solutions at infinity for symplectic systems on time scales. Zbl 1474.34629
Drimalova, Iva; Šimon Hilscher, Roman
2
2020
Comparative index and Lidskii angles for symplectic matrices. Zbl 1467.37055
Šepitka, Peter; Šimon Hilscher, Roman
2
2021
On square integrable solutions and principal and antiprincipal solutions for linear Hamiltonian systems. Zbl 1383.34043
Šimon Hilscher, Roman; Zemánek, Petr
2
2018
Oscillation numbers for continuous Lagrangian paths and Maslov index. Zbl 1530.37087
Elyseeva, Julia; Šepitka, Peter; Šimon Hilscher, Roman
2
2023
On disconjugacy for vector linear Hamiltonian systems on time scales. Zbl 1183.34047
Hilscher, Roman
1
2000
Comparison results for solutions of time scale matrix Riccati equations and inequalities. Zbl 1171.34313
Hilscher, R.
1
2006
Eigenvalue comparison for discrete symplectic systems. Zbl 1336.39009
Šimon Hilscher, Roman
1
2015
Comparison theorems for self-adjoint linear Hamiltonian eigenvalue problems. Zbl 1297.34048
Šimon Hilscher, Roman
1
2014
Sturm-Liouville matrix differential systems with singular leading coefficient. Zbl 1392.34021
Dřímalová, Iva; Kratz, Werner; Šimon Hilscher, Roman
1
2017
Oscillation numbers for continuous Lagrangian paths and Maslov index. Zbl 1530.37087
Elyseeva, Julia; Šepitka, Peter; Šimon Hilscher, Roman
2
2023
Solutions with prescribed numbers of focal points of nonoscillatory linear Hamiltonian systems. Zbl 1511.37061
Šepitka, Peter; Šimon Hilscher, Roman
1
2023
Distribution and number of focal points for linear Hamiltonian systems. Zbl 1460.37082
Šepitka, Peter; Šimon Hilscher, Roman
4
2021
Lidskii angles and Sturmian theory for linear Hamiltonian systems on compact interval. Zbl 1478.37057
Šepitka, Peter; Šimon Hilscher, Roman
2
2021
Comparative index and Lidskii angles for symplectic matrices. Zbl 1467.37055
Šepitka, Peter; Šimon Hilscher, Roman
2
2021
Singular Sturmian comparison theorems for linear Hamiltonian systems. Zbl 1442.37114
Šepitka, Peter; Šimon Hilscher, Roman
8
2020
Sturmian comparison theorems for completely controllable linear Hamiltonian systems in singular case. Zbl 1439.37088
Šepitka, Peter; Šimon Hilscher, Roman
3
2020
Antiprincipal solutions at infinity for symplectic systems on time scales. Zbl 1474.34629
Drimalova, Iva; Šimon Hilscher, Roman
2
2020
Symplectic difference systems: oscillation and spectral theory. Zbl 1425.39001
Došlý, Ondřej; Elyseeva, Julia; Šimon Hilscher, Roman
19
2019
Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems. Zbl 1408.37107
Šepitka, Peter; Šimon Hilscher, Roman
8
2019
Focal points and principal solutions of linear Hamiltonian systems revisited. Zbl 1394.34061
Šepitka, Peter; Šimon Hilscher, Roman
10
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
9
2018
Sufficiency and sensitivity for nonlinear optimal control problems on time scales via coercivity. Zbl 1415.49015
Šimon Hilscher, Roman; Zeidan, Vera
4
2018
Singular Sturmian separation theorems for nonoscillatory symplectic difference systems. Zbl 1405.39006
Šepitka, Peter; Šimon Hilscher, Roman
4
2018
On square integrable solutions and principal and antiprincipal solutions for linear Hamiltonian systems. Zbl 1383.34043
Šimon Hilscher, Roman; Zemánek, Petr
2
2018
Comparative index and Sturmian theory for linear Hamiltonian systems. Zbl 1375.34052
Šepitka, Peter; Šimon Hilscher, Roman
22
2017
Dominant and recessive solutions at infinity and genera of conjoined bases for discrete symplectic systems. Zbl 1376.39004
Šepitka, Peter; Šimon Hilscher, Roman
5
2017
Sturm-Liouville matrix differential systems with singular leading coefficient. Zbl 1392.34021
Dřímalová, Iva; Kratz, Werner; Šimon Hilscher, Roman
1
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
12
2016
Reid’s construction of minimal principal solution at infinity for linear Hamiltonian systems. Zbl 1375.37058
Šepitka, Peter; Šimon Hilscher, Roman
8
2016
Principal solutions at infinity for time scale symplectic systems without controllability condition. Zbl 1343.93057
Šepitka, Peter; Šimon Hilscher, Roman
4
2016
Principal solutions at infinity of given ranks for nonoscillatory linear Hamiltonian systems. Zbl 1348.37091
Šepitka, Peter; Šimon Hilscher, Roman
20
2015
Principal and antiprincipal solutions at infinity of linear Hamiltonian systems. Zbl 1329.34024
Šepitka, Peter; Šimon Hilscher, Roman
16
2015
Limit circle invariance for two differential systems on time scales. Zbl 1312.34142
Šimon Hilscher, Roman; Zemánek, Petr
11
2015
Time scale symplectic systems with analytic dependence on spectral parameter. Zbl 1312.34141
Šimon Hilscher, Roman; Zemánek, Petr
5
2015
Recessive solutions for nonoscillatory discrete symplectic systems. Zbl 1307.39007
Šepitka, Peter; Šimon Hilscher, Roman
5
2015
Asymptotic properties of solutions of Riccati matrix equations and inequalities for discrete symplectic systems. Zbl 1349.39021
Šimon Hilscher, R.
2
2015
Eigenvalue comparison for discrete symplectic systems. Zbl 1336.39009
Šimon Hilscher, Roman
1
2015
Minimal principal solution at infinity for nonoscillatory linear Hamiltonian systems. Zbl 1305.34053
Šepitka, Peter; Šimon Hilscher, Roman
28
2014
Weyl-Titchmarsh theory for discrete symplectic systems with general linear dependence on spectral parameter. Zbl 1312.39011
Šimon Hilscher, Roman; Zemánek, Petr
19
2014
Limit point and limit circle classification for symplectic systems on time scales. Zbl 1334.34197
Šimon Hilscher, Roman; Zemánek, Petr
18
2014
Generalized Lagrange identity for discrete symplectic systems and applications in Weyl-Titchmarsh theory. Zbl 1318.39008
Šimon Hilscher, Roman; Zemánek, Petr
6
2014
Comparison theorems for self-adjoint linear Hamiltonian eigenvalue problems. Zbl 1297.34048
Šimon Hilscher, Roman
1
2014
A generalized index theorem for monotone matrix-valued functions with applications to discrete oscillation theory. Zbl 1365.39009
Kratz, W.; Šimon Hilscher, R.
8
2013
Weyl disks and square summable solutions for discrete symplectic systems with jointly varying endpoints. Zbl 1375.39014
Šimon Hilscher, Roman; Zemánek, Petr
6
2013
Rayleigh principle for linear Hamiltonian systems without controllability. Zbl 1254.34120
Kratz, Werner; Šimon Hilscher, Roman
22
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
14
2012
Hamilton-Jacobi theory over time scales and applications to linear-quadratic problems. Zbl 1230.49023
Šimon Hilscher, Roman; Zeidan, Vera
13
2012
Spectral and oscillation theory for general second order Sturm-Liouville difference equations. Zbl 1302.39022
Šimon Hilscher, Roman
13
2012
Oscillation theorems for discrete symplectic systems with nonlinear dependence in spectral parameter. Zbl 1258.39005
Šimon Hilscher, Roman
12
2012
Eigenvalue theory for time scale symplectic systems depending nonlinearly on spectral parameter. Zbl 1309.34148
Šimon Hilscher, Roman
7
2012
Oscillation theorems and Rayleigh principle for linear Hamiltonian and symplectic systems with general boundary conditions. Zbl 1257.34077
Šimon Hilscher, Roman; Zeidan, Vera
7
2012
Oscillation criterion for half-linear differential equations with periodic coefficients. Zbl 1258.34064
Došlý, O.; Özbekler, A.; Šimon Hilscher, R.
7
2012
New results for time reversed symplectic dynamic systems and quadratic functionals. Zbl 1324.34195
Šimon Hilscher, R.; Zemánek, Petr
4
2012
Sturmian theory for linear Hamiltonian systems without controllability. Zbl 1218.34038
Šimon Hilscher, Roman
27
2011
On general Sturmian theory for abnormal linear Hamiltonian systems. Zbl 1306.34051
Šimon Hilscher, Roman
22
2011
Eigenvalue and oscillation theorems for time scale symplectic systems. Zbl 1218.34039
Kratz, Werner; Šimon Hilscher, Roman; Zeidan, Vera Michel
13
2011
Weyl-Titchmarsh theory for time scale symplectic systems on half line. Zbl 1217.34144
Šimon Hilscher, Roman; Zemánek, Petr
11
2011
First order conditions for generalized variational problems over time scales. Zbl 1236.49061
Šimon Hilscher, Roman; Zeidan, Vera
8
2011
Rayleigh principle for time scale symplectic systems and applications. Zbl 1340.34355
Šimon Hilscher, Roman; Zeidan, Vera
8
2011
Friedrichs extension of operators defined by linear Hamiltonian systems on unbounded interval. Zbl 1220.47028
Šimon Hilscher, Roman; Zemánek, Petr
9
2010
Symmetric three-term recurrence equations and their symplectic structure. Zbl 1198.39002
Šimon Hilscher, Roman; Zeidan, Vera
8
2010
Reid roundabout theorems for time scale symplectic systems. Zbl 1229.34138
Hilscher, R.; Zeidan, V.
4
2010
Nabla time scale symplectic systems and related quadratic functionals. Zbl 1214.34091
Hilscher, Roman; Zeidan, Vera
3
2010
Weak maximum principle and accessory problem for control problems on time scales. Zbl 1157.49030
Hilscher, Roman; Zeidan, Vera
35
2009
Multiplicities of focal points for discrete symplectic systems: revisited. Zbl 1188.39005
Hilscher, Roman; Zeidan, Vera
7
2009
Picone type identities and definiteness of quadratic functionals on time scales. Zbl 1178.93094
Šimon Hilscher, Roman; Zeidan, Vera
4
2009
Trigonometric and hyperbolic systems on time scales. Zbl 1184.34089
Hilscher, R.; Zemánek, P.
3
2009
Applications of time scale symplectic systems without normality. Zbl 1145.39006
Hilscher, Roman; Zeidan, Vera
18
2008
Riccati equations for abnormal time scale quadratic functionals. Zbl 1355.49031
Hilscher, Roman; Zeidan, Vera
17
2008
Time scale embedding theorem and coercivity of quadratic functionals. Zbl 1136.49017
Hilscher, Roman; Zeidan, Vera
15
2008
Terminal value problems for first and second order nonlinear equations on time scales. Zbl 1176.34059
Hilscher, Roman; Tisdell, Christopher C.
3
2008
Legendre, Jacobi, and Riccati type conditions for time scale variational problem with application. Zbl 1160.39004
Hilscher, R.; Zeidan, V.
6
2007
Perturbation of nonnegative time scale quadratic functionals. Zbl 1127.39032
Hilscher, R.; Růžičková, V.
2
2007
Riccati inequality and other results for discrete symplectic systems. Zbl 1103.39020
Hilscher, Roman; Růžičková, Viera
14
2006
Time scale symplectic systems without normality. Zbl 1104.37037
Hilscher, Roman; Zeidan, Vera
14
2006
Implicit Riccati equations and quadratic functionals for discrete symplectic systems. Zbl 1112.39007
Hilscher, Roman; Růžičková, Viera
11
2006
Coupled intervals for discrete symplectic systems. Zbl 1115.39019
Hilscher, Roman; Zeidan, Vera
6
2006
Comparison results for solutions of time scale matrix Riccati equations and inequalities. Zbl 1171.34313
Hilscher, R.
1
2006
Nonnegativity and positivity of quadratic functionals in discrete calculus of variations: survey. Zbl 1098.49025
Hilscher, Roman; Zeidan, Vera
15
2005
An eigenvalue problem for linear Hamiltonian dynamic systems. Zbl 1096.39017
Bohner, Martin; Hilscher, Roman
8
2005
Solvability of the discrete LQR-problem under minimal assumptions. Zbl 1094.39018
Hilscher, Roman; Zeidan, Vera
2
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
47
2004
Equivalent conditions to the nonnegativity of a quadratic functional in discrete optimal control. Zbl 1042.39007
Hilscher, Roman; Zeidan, Vera
4
2004
Coupled intervals in the discrete optimal control. Zbl 1051.39017
Hilscher, Roman; Zeidan, Vera
4
2004
Discrete quadratic functionals with jointly varying endpoints via separable endpoints. Zbl 1065.39033
Hilscher, Roman; Zeidan, Vera
2
2004
Symplectic difference systems: Variable stepsize discretization and discrete quadratic functionals. Zbl 1021.39008
Hilscher, Roman; Zeidan, Vera
22
2003
Nonnegativity of discrete quadratic functionals corresponding to symplectic difference systems. Zbl 1056.39020
Došlý, Ondřej; Hilscher, Roman; Zeidan, Vera
9
2003
A class of Sturm-Liouville difference equations: (Non)oscillation constants and property BD. Zbl 1054.39013
Došlý, O.; Hilscher, R.
7
2003
Diagonalization approach to discrete quadratic functionals. Zbl 1033.39003
Bohner, M.; Došlý, O.; Hilscher, R.; Kratz, W.
5
2003
Nonnegativity of a discrete quadratic functional in terms of the (strengthened) Legendre and Jacobi conditions. Zbl 1044.49020
Hilscher, R.; Zeidan, V.
4
2003
Riccati inequality, disconjugacy, and reciprocity principle for linear Hamiltonian dynamic systems. Zbl 1046.39009
Hilscher, Roman; Řehák, Pavel
4
2003
A remark on discrete quadratic functionals with separable endpoints. Zbl 1058.39013
Hilscher, Roman; Zeidan, Vera
3
2003
Second order sufficiency criteria for a discrete optimal control problem. Zbl 1010.49020
Hilscher, Roman; Zeidan, Vera
24
2002
Discrete optimal control: Second order optimality conditions. Zbl 1010.49021
Hilscher, Roman; Zeidan, Vera
21
2002
A time scales version of a Wirtinger-type inequality and applications. Zbl 1025.26012
Hilscher, Roman
21
2002
Coupled intervals in the discrete calculus of variations: necessity and sufficiency. Zbl 1032.49038
Hilscher, Roman; Zeidan, Vera
7
2002
Disconjugacy, transformations and quadratic functionals for symplectic dynamic systems on time scales. Zbl 0989.34027
Došlý, Ondřej; Hilscher, Roman
28
2001
Reid roundabout theorem for symplectic dynamic systems on time scales. Zbl 0990.39017
Hilscher, R.
23
2001
Linear Hamiltonian dynamic systems on time scales: Sturmian property of the principal solution. Zbl 1042.34509
Bohner, M.; Došlý, O.; Hilscher, R.
13
2001
Discrete spectra criteria for certain classes of singular differential and difference operators. Zbl 1008.39011
Hilscher, R.
12
2001
Positivity of quadratic functionals on time scales: Necessity. Zbl 0999.34037
Hilscher, Roman
6
2001
Inhomogeneous quadratic functionals on time scales. Zbl 0974.39008
Hilscher, Roman
2
2001
Linear Hamiltonian systems on time scales: Positivity of quadratic functionals. Zbl 0982.37054
Hilscher, R.
11
2000
Discrete optimal control: The accessory problem and necessary optimality conditions. Zbl 0987.49016
Hilscher, Roman; Zeidan, Vera
10
2000
Spectral properties of general selfadjoint, even-order differential operators. Zbl 0995.34077
Hilscher, Roman
3
2000
On disconjugacy for vector linear Hamiltonian systems on time scales. Zbl 1183.34047
Hilscher, Roman
1
2000
Disconjugacy of symplectic systems and positive definiteness of block tridiagonal matrices. Zbl 0956.39010
Hilscher, Roman
12
1999
Linear Hamiltonian difference systems: Transformations, recessive solutions, generalized reciprocity. Zbl 0946.39003
Došlý, Ondřej; Hilscher, Roman
9
1999
Linear Hamiltonian systems on time scales: Transformations. Zbl 0997.34005
Hilscher, Roman
3
1999
...and 1 more Documents
all top 5

Cited by 293 Authors

67 Šimon Hilscher, Roman
24 Zeidan, Vera Michel
22 Šepitka, Peter
18 Došlý, Ondřej
18 Zemánek, Petr
16 Elyseeva, Julia V.
11 Bohner, Martin J.
9 Eldeeb, Ahmed Abdel-Moneim
8 Kratz, Werner
8 Marinković, Boban
6 Shi, Yuming
6 Zhang, Yi
5 Bartosiewicz, Zbigniew
5 Mardanov, Misir Dzhumail ogly
5 Nguyen Thi Toan
5 Ren, Guojing
5 Sugie, Jitsuro
5 Sun, Huaqing
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 Migda, Janusz
4 Ngô Quốc Anh
4 Núñez Jiménez, Carmen
4 Sakhnovich, Alexander L.
4 Song, Chuanjing
4 Thuy, Le Quang
4 Ugurlu, Ekin
3 Bourdin, Loïc
3 Dřímalová, Iva
3 Elsennary, Hamza A.
3 Gao, Chenghua
3 Gavrikov, Alexander A.
3 Ishibashi, Kazuki
3 Jia, Guangyan
3 Khan, Zareen Abdulhameed
3 Lv, Weidong
3 Melikov, Telman Kuli
3 Obaya, Rafael
3 Řehák, Pavel
3 Schulz-Baldes, Hermann
3 Wei, Wei
3 Zhan, Zaidong
3 Zheng, Zhaowen
3 Zhou, Zhan
3 Zhu, Yingjun
2 Agarwal, Ravi P.
2 Ahlbrandt, Calvin D.
2 Akulenko, Leonid Denisovich
2 Anderson, Douglas Robert
2 Bairamov, Elgiz
2 dos Santos, Iguer Luis Domini
2 Fabbri, Roberta
2 Ferreira, Rui A. C.
2 Fu, Jingli
2 Grow, David E.
2 Guseinov, Gusein Sh.
2 Hasil, Petr
2 Heidarkhani, Shapour
2 Hilger, Stefan
2 Jiang, Liqun
2 Khan, Asif Raza
2 Kong, Qingkai
2 Kotta, Ulle
2 Mahmudov, Elimhan Nadir
2 Mahmudov, Nazim Idrisoglu
2 Mehmood, Faraz
2 Merdivenci Atici, Ferhan
2 Migda, Małgorzata
2 Nesterov, Sergeĭ V.
2 Nockowska-Rosiak, Magdalena
2 Novo, Sylvia
2 Nwaeze, Eze Raymond
2 Ozkan, Ahmet Sinan
2 Pawłuszewicz, Ewa
2 Peng, Yunfei
2 Saker, Samir H.
2 Shaikh, Muhammad Awais
2 Shao, Jing
2 Sun, Shurong
2 Trélat, Emmanuel
2 Wintz, Nick
2 Wyrwas, Małgorzata
2 Xiang, Xiaoling
2 Yamaoka, Naoto
2 Yang, Chen
2 Zhai, Xianghua
2 Zhang, Chao
2 Zhang, Fei
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
...and 193 more Authors
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Cited in 112 Serials

26 Journal of Mathematical Analysis and Applications
22 Applied Mathematics and Computation
22 Advances in Difference Equations
20 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
8 Mathematische Nachrichten
7 Journal of Computational and Applied Mathematics
7 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
6 Journal of Dynamics and Differential Equations
5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
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 Monatshefte für Mathematik
3 Discrete and Continuous Dynamical Systems
3 Positivity
3 Differential Equations
2 Mathematica Slovaca
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2 Quaestiones Mathematicae
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2 Filomat
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2 Journal of Inequalities and Applications
2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
2 Nonlinear Analysis. Hybrid Systems
2 Differential Equations and Applications
1 International Journal of Control
1 International Journal of Theoretical Physics
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1 Journal of the Franklin Institute
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1 Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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1 The ANZIAM Journal
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1 Vladikavkazskiĭ Matematicheskiĭ Zhurnal
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