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## Šimon Hilscher, Roman

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 Author ID: simon-hilscher.roman Published as: Hilscher, R.; Hilscher, Roman; Hilscher, Roman Šimon; Šimon Hilscher, R.; Šimon Hilscher, Roman Homepage: https://www.math.muni.cz/~hilscher/ External Links: MGP · ORCID · dblp
 Documents Indexed: 101 Publications since 1997, including 2 Books Reviewing Activity: 159 Reviews
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#### Co-Authors

 21 single-authored 33 Zeidan, Vera Michel 15 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 8 Journal of Differential Equations 7 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 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Advances in Difference Equations 2 Rocky Mountain Journal of Mathematics 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Mathematica Bohemica 2 Journal of Dynamics and Differential Equations 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 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 Difference and functional equations (39-XX) 59 Ordinary differential equations (34-XX) 38 Dynamical systems and ergodic theory (37-XX) 21 Calculus of variations and optimal control; optimization (49-XX) 21 Systems theory; control (93-XX) 9 Linear and multilinear algebra; matrix theory (15-XX) 5 Operator theory (47-XX) 3 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 Numerical analysis (65-XX) 1 Mechanics of particles and systems (70-XX)

#### Citations contained in zbMATH

90 Publications have been cited 740 times in 242 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
Disconjugacy, transformations and quadratic functionals for symplectic dynamic systems on time scales. Zbl 0989.34027
Došlý, Ondřej; Hilscher, Roman
2001
Weak maximum principle and accessory problem for control problems on time scales. Zbl 1157.49030
Hilscher, Roman; Zeidan, Vera
2009
Minimal principal solution at infinity for nonoscillatory linear Hamiltonian systems. Zbl 1305.34053
Šepitka, Peter; Šimon Hilscher, Roman
2014
Sturmian theory for linear Hamiltonian systems without controllability. Zbl 1218.34038
Šimon Hilscher, Roman
2011
Symplectic difference systems: Variable stepsize discretization and discrete quadratic functionals. Zbl 1021.39008
Hilscher, Roman; Zeidan, Vera
2003
Second order sufficiency criteria for a discrete optimal control problem. Zbl 1010.49020
Hilscher, Roman; Zeidan, Vera
2002
Reid roundabout theorem for symplectic dynamic systems on time scales. Zbl 0990.39017
Hilscher, R.
2001
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
Principal solutions at infinity of given ranks for nonoscillatory linear Hamiltonian systems. Zbl 1348.37091
Šepitka, Peter; Šimon Hilscher, Roman
2015
Nonnegativity and positivity of quadratic functionals in discrete calculus of variations: survey. Zbl 1098.49025
Hilscher, Roman; Zeidan, Vera
2005
On general Sturmian theory for abnormal linear Hamiltonian systems. Zbl 1306.34051
Šimon Hilscher, Roman
2011
Riccati equations for abnormal time scale quadratic functionals. Zbl 1355.49031
Hilscher, Roman; Zeidan, Vera
2008
Applications of time scale symplectic systems without normality. Zbl 1145.39006
Hilscher, Roman; Zeidan, Vera
2008
Weyl-Titchmarsh theory for discrete symplectic systems with general linear dependence on spectral parameter. Zbl 1312.39011
Šimon Hilscher, Roman; Zemánek, Petr
2014
A time scales version of a Wirtinger-type inequality and applications. Zbl 1025.26012
Hilscher, Roman
2002
Time scale embedding theorem and coercivity of quadratic functionals. Zbl 1136.49017
Hilscher, Roman; Zeidan, Vera
2008
Time scale symplectic systems without normality. Zbl 1104.37037
Hilscher, Roman; Zeidan, Vera
2006
Riccati inequality and other results for discrete symplectic systems. Zbl 1103.39020
Hilscher, Roman; Růžičková, Viera
2006
Disconjugacy of symplectic systems and positive definiteness of block tridiagonal matrices. Zbl 0956.39010
Hilscher, Roman
1999
Principal and antiprincipal solutions at infinity of linear Hamiltonian systems. Zbl 1329.34024
Šepitka, Peter; Šimon Hilscher, Roman
2015
Limit point and limit circle classification for symplectic systems on time scales. Zbl 1334.34197
Šimon Hilscher, Roman; Zemánek, Petr
2014
Oscillation theorems for discrete symplectic systems with nonlinear dependence in spectral parameter. Zbl 1258.39005
Šimon Hilscher, Roman
2012
Eigenvalue and oscillation theorems for time scale symplectic systems. Zbl 1218.34039
Kratz, Werner; Šimon Hilscher, Roman; Zeidan, Vera Michel
2011
Linear Hamiltonian dynamic systems on time scales: Sturmian property of the principal solution. Zbl 1042.34509
Bohner, M.; Došlý, O.; Hilscher, R.
2001
Discrete spectra criteria for certain classes of singular differential and difference operators. Zbl 1008.39011
Hilscher, R.
2001
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
Nonnegativity of discrete quadratic functionals corresponding to symplectic difference systems. Zbl 1056.39020
Došlý, Ondřej; Hilscher, Roman; Zeidan, Vera
2003
Linear Hamiltonian difference systems: Transformations, recessive solutions, generalized reciprocity. Zbl 0946.39003
Došlý, Ondřej; Hilscher, Roman
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
2016
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
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
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
A generalized index theorem for monotone matrix-valued functions with applications to discrete oscillation theory. Zbl 1365.39009
Kratz, W.; Šimon Hilscher, R.
2013
Coupled intervals in the discrete calculus of variations: necessity and sufficiency. Zbl 1032.49038
Hilscher, Roman; Zeidan, Vera
2002
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
Oscillation criterion for half-linear differential equations with periodic coefficients. Zbl 1258.34064
Došlý, O.; Özbekler, A.; Šimon Hilscher, R.
2012
Hamilton-Jacobi theory over time scales and applications to linear-quadratic problems. Zbl 1230.49023
Šimon Hilscher, Roman; Zeidan, Vera
2012
Rayleigh principle for time scale symplectic systems and applications. Zbl 1340.34355
Šimon Hilscher, Roman; Zeidan, Vera
2011
First order conditions for generalized variational problems over time scales. Zbl 1236.49061
Šimon Hilscher, Roman; Zeidan, Vera
2011
Friedrichs extension of operators defined by linear Hamiltonian systems on unbounded interval. Zbl 1220.47028
Šimon Hilscher, Roman; Zemánek, Petr
2010
Nabla time scale symplectic systems and related quadratic functionals. Zbl 1214.34091
Hilscher, Roman; Zeidan, Vera
2010
Multiplicities of focal points for discrete symplectic systems: revisited. Zbl 1188.39005
Hilscher, Roman; Zeidan, Vera
2009
Legendre, Jacobi, and Riccati type conditions for time scale variational problem with application. Zbl 1160.39004
Hilscher, R.; Zeidan, V.
2007
Coupled intervals for discrete symplectic systems. Zbl 1115.39019
Hilscher, Roman; Zeidan, Vera
2006
A class of Sturm-Liouville difference equations: (Non)oscillation constants and property BD. Zbl 1054.39013
Došlý, O.; Hilscher, R.
2003
Positivity of quadratic functionals on time scales: Necessity. Zbl 0999.34037
Hilscher, Roman
2001
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
Focal points and principal solutions of linear Hamiltonian systems revisited. Zbl 1394.34061
Šepitka, Peter; Šimon Hilscher, Roman
2018
Reid’s construction of minimal principal solution at infinity for linear Hamiltonian systems. Zbl 1375.37058
Šepitka, Peter; Šimon Hilscher, Roman
2016
Limit circle invariance for two differential systems on time scales. Zbl 1312.34142
Šimon Hilscher, Roman; Zemánek, Petr
2015
Eigenvalue theory for time scale symplectic systems depending nonlinearly on spectral parameter. Zbl 1309.34148
Šimon Hilscher, Roman
2012
Diagonalization approach to discrete quadratic functionals. Zbl 1033.39003
Bohner, M.; Došlý, O.; Hilscher, R.; Kratz, W.
2003
Symplectic difference systems: oscillation and spectral theory. Zbl 1425.39001
Došlý, Ondřej; Elyseeva, Julia; Hilscher, Roman Šimon
2019
Weyl disks and square summable solutions for discrete symplectic systems with jointly varying endpoints. Zbl 1375.39014
Hilscher, Roman Šimon; Zemánek, Petr
2013
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
Coupled intervals in the discrete optimal control. Zbl 1051.39017
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
Nonnegativity of a discrete quadratic functional in terms of the (strengthened) Legendre and Jacobi conditions. Zbl 1044.49020
Hilscher, R.; Zeidan, V.
2003
Riccati inequality, disconjugacy, and reciprocity principle for linear Hamiltonian dynamic systems. Zbl 1046.39009
Hilscher, Roman; Řehák, Pavel
2003
Spectral properties of fourth order differential operators. Zbl 0894.34028
Došlý, O.; Hilscher, R.
1997
Generalized Lagrange identity for discrete symplectic systems and applications in Weyl-Titchmarsh theory. Zbl 1318.39008
Šimon Hilscher, Roman; Zemánek, Petr
2014
New results for time reversed symplectic dynamic systems and quadratic functionals. Zbl 1324.34195
Šimon Hilscher, R.; Zemánek, Petr
2012
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
A remark on discrete quadratic functionals with separable endpoints. Zbl 1058.39013
Hilscher, Roman; Zeidan, Vera
2003
Spectral properties of general selfadjoint, even-order differential operators. Zbl 0995.34077
Hilscher, Roman
2000
Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems. Zbl 1408.37107
Šepitka, Peter; Šimon Hilscher, Roman
2019
Dominant and recessive solutions at infinity and genera of conjoined bases for discrete symplectic systems. Zbl 1376.39004
Šepitka, Peter; Hilscher, Roman Šimon
2017
Principal solutions at infinity for time scale symplectic systems without controllability condition. Zbl 1343.93057
Šepitka, Peter; Šimon Hilscher, Roman
2016
Time scale symplectic systems with analytic dependence on spectral parameter. Zbl 1312.34141
Šimon Hilscher, Roman; Zemánek, Petr
2015
Recessive solutions for nonoscillatory discrete symplectic systems. Zbl 1307.39007
Šepitka, Peter; Šimon Hilscher, Roman
2015
Perturbation of nonnegative time scale quadratic functionals. Zbl 1127.39032
Hilscher, R.; Růžičková, V.
2007
Solvability of the discrete LQR-problem under minimal assumptions. Zbl 1094.39018
Hilscher, Roman; Zeidan, Vera
2005
Discrete quadratic functionals with jointly varying endpoints via separable endpoints. Zbl 1065.39033
Hilscher, Roman; Zeidan, Vera
2004
Inhomogeneous quadratic functionals on time scales. Zbl 0974.39008
Hilscher, Roman
2001
Linear Hamiltonian systems on time scales: Transformations. Zbl 0997.34005
Hilscher, Roman
1999
Sufficiency and sensitivity for nonlinear optimal control problems on time scales via coercivity. Zbl 1415.49015
Hilscher, Roman Šimon; Zeidan, Vera
2018
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
Comparison theorems for self-adjoint linear Hamiltonian eigenvalue problems. Zbl 1297.34048
Šimon Hilscher, Roman
2014
Comparison results for solutions of time scale matrix Riccati equations and inequalities. Zbl 1171.34313
Hilscher, R.
2006
On disconjugacy for vector linear Hamiltonian systems on time scales. Zbl 1183.34047
Hilscher, Roman
2000
Symplectic difference systems: oscillation and spectral theory. Zbl 1425.39001
Došlý, Ondřej; Elyseeva, Julia; Hilscher, Roman Šimon
2019
Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems. Zbl 1408.37107
Šepitka, Peter; Šimon Hilscher, Roman
2019
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
Focal points and principal solutions of linear Hamiltonian systems revisited. Zbl 1394.34061
Šepitka, Peter; Šimon Hilscher, Roman
2018
Sufficiency and sensitivity for nonlinear optimal control problems on time scales via coercivity. Zbl 1415.49015
Hilscher, Roman Šimon; Zeidan, Vera
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; Hilscher, Roman Šimon
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
Time scale symplectic systems with analytic dependence on spectral parameter. Zbl 1312.34141
Šimon Hilscher, Roman; Zemánek, Petr
2015
Recessive solutions for nonoscillatory discrete symplectic systems. Zbl 1307.39007
Šepitka, Peter; Šimon Hilscher, Roman
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
Hilscher, Roman Šimon; Zemánek, Petr
2013
Rayleigh principle for linear Hamiltonian systems without controllability. Zbl 1254.34120
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
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
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
Oscillation criterion for half-linear differential equations with periodic coefficients. Zbl 1258.34064
Došlý, O.; Özbekler, A.; Šimon Hilscher, R.
2012
Hamilton-Jacobi theory over time scales and applications to linear-quadratic problems. Zbl 1230.49023
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
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
Rayleigh principle for time scale symplectic systems and applications. Zbl 1340.34355
Šimon Hilscher, Roman; Zeidan, Vera
2011
First order conditions for generalized variational problems over time scales. Zbl 1236.49061
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
Nabla time scale symplectic systems and related quadratic functionals. Zbl 1214.34091
Hilscher, Roman; Zeidan, Vera
2010
Reid roundabout theorems for time scale symplectic systems. Zbl 1229.34138
Hilscher, R.; Zeidan, V.
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
Riccati equations for abnormal time scale quadratic functionals. Zbl 1355.49031
Hilscher, Roman; Zeidan, Vera
2008
Applications of time scale symplectic systems without normality. Zbl 1145.39006
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
Time scale symplectic systems without normality. Zbl 1104.37037
Hilscher, Roman; Zeidan, Vera
2006
Riccati inequality and other results for discrete symplectic systems. Zbl 1103.39020
Hilscher, Roman; Růžičková, Viera
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
Coupled intervals in the discrete optimal control. Zbl 1051.39017
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
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
Nonnegativity of a discrete quadratic functional in terms of the (strengthened) Legendre and Jacobi conditions. Zbl 1044.49020
Hilscher, R.; Zeidan, V.
2003
Riccati inequality, disconjugacy, and reciprocity principle for linear Hamiltonian dynamic systems. Zbl 1046.39009
Hilscher, Roman; Řehák, Pavel
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
Discrete optimal control: Second order optimality conditions. Zbl 1010.49021
Hilscher, Roman; Zeidan, Vera
2002
A time scales version of a Wirtinger-type inequality and applications. Zbl 1025.26012
Hilscher, Roman
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
Linear Hamiltonian dynamic systems on time scales: Sturmian property of the principal solution. Zbl 1042.34509
Bohner, M.; Došlý, O.; Hilscher, R.
2001
Discrete spectra criteria for certain classes of singular differential and difference operators. Zbl 1008.39011
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 221 Authors

 60 Šimon Hilscher, Roman 23 Zeidan, Vera Michel 20 Došlý, Ondřej 16 Šepitka, Peter 14 Elyseeva, Julia V. 14 Zemánek, Petr 9 Bohner, Martin J. 9 Kratz, Werner 8 Marinković, Boban 6 Shi, Yuming 5 Bartosiewicz, Zbigniew 5 Mardanov, Misir Dzhumail ogly 5 Sugie, Jitsuro 5 Torres, Delfim Fernando Marado 4 Liu, Wenjun J. 4 Malik, Samin T. 4 Ngo, Quoc Anh 4 Núñez, Carmen A. 4 Ren, Guojing 4 Song, Chuanjing 4 Zhang, Yi 3 Clark, Stephen L. 3 Gavrikov, Alexander A. 3 Lv, Weidong 3 Malinowska, Agnieszka Barbara 3 Martins, Natália F. 3 Melikov, Telman Kuli 3 Nguyen Thi Toan 3 Obaya, Rafael 3 Řehák, Pavel 3 Sun, Huaqing 3 Ugurlu, Ekin 3 Wei, Wei 3 Zhan, Zaidong 3 Zhou, Zhan 2 Ahlbrandt, Calvin D. 2 Akulenko, Leonid Denisovich 2 Anderson, Douglas Robert 2 Bourdin, Loïc 2 Eldeeb, Ahmed Abdel-Moneim 2 Elsennary, H. A. 2 Fabbri, Roberta 2 Ferreira, Rui A. C. 2 Guseinov, Gusein Sh. 2 Hasil, Petr 2 Hilger, Stefan 2 Ishibashi, Kazuki 2 Jiang, Liqun 2 Kong, Qingkai 2 Kotta, Ulle 2 Mahmudov, Nazim Idrisoglu 2 Merdivenci Atici, Ferhan 2 Nesterov, Sergeĭ V. 2 Novo, Sylvia 2 Ozkan, Ahmet Sinan 2 Pawłuszewicz, Ewa 2 Peng, Yunfei 2 Sakhnovich, Alexander L. 2 Sun, Shurong 2 Thuy, Le Quang 2 Trélat, Emmanuel 2 Wyrwas, Małgorzata 2 Xiang, Xiaoling 2 Yamaoka, Naoto 2 Zhang, Chao 2 Zheng, Zhaowen 1 Adalar, Ibrahim 1 Adivar, Murat 1 Agarwal, Praveen 1 Agarwal, Ravi P. 1 Aliyev, Ziyatkhan S. 1 Alomari, Mohammad Wajeeh 1 Anerot, Baptiste 1 Ansari, Qamrul Hasan 1 Bairamov, Elgiz 1 Bajaj, Chanderjit L. 1 Bastos, Nuno R. O. 1 Belikov, Juri 1 Bidgoli, Tayebeh Aliabdoli 1 Biles, Daniel C. 1 Cabada, Alberto 1 Cai, Ping-ping 1 Chen, Shaozhu 1 Chen, Wenbing 1 Cheng, Yao 1 Cresson, Jacky 1 Cuchta, Tom 1 Cveticanin, L. J. 1 Daghan, Durmus 1 Davis, John M. 1 Deng, XunHuan 1 Ding, Xiaohua 1 Đukić, Đorđe Slavka 1 dos Santos, Iguer Luis Domini 1 Dřímalová, Iva 1 Duc, Dinh Thanh 1 Eliseeva, Yu. V. 1 Fan, Yonghong 1 Fang, Shu-Cherng 1 Fang, Zhongbo ...and 121 more Authors
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#### Cited in 81 Serials

 25 Journal of Mathematical Analysis and Applications 19 Journal of Difference Equations and Applications 18 Advances in Difference Equations 17 Applied Mathematics and Computation 12 Applied Mathematics Letters 11 Computers & Mathematics with Applications 10 Journal of Differential Equations 10 Linear Algebra and its Applications 8 Journal of Computational and Applied Mathematics 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 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Journal of Optimization Theory and Applications 3 Discrete Dynamics in Nature and Society 2 Rocky Mountain Journal of Mathematics 2 Mathematica Slovaca 2 Monatshefte für Mathematik 2 Numerical Functional Analysis and Optimization 2 Mathematical and Computer Modelling 2 Complexity 2 Positivity 2 Differential Equations 2 Boundary Value Problems 2 Nonlinear Analysis. Hybrid Systems 1 International Journal of Control 1 Inverse Problems 1 Journal of the Franklin Institute 1 Mathematical Notes 1 Moscow University Mechanics Bulletin 1 Reports on Mathematical Physics 1 Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 1 Automatica 1 Fasciculi Mathematici 1 International Journal of Mathematics and Mathematical Sciences 1 Integral Equations and Operator Theory 1 Meccanica 1 Quaestiones Mathematicae 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 Journal of Global Optimization 1 Computational Mathematics and Mathematical Physics 1 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 1 Computational and Applied Mathematics 1 Journal of Inverse and Ill-Posed Problems 1 Opuscula Mathematica 1 Discrete and Continuous Dynamical Systems 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 Computational Methods and Function Theory 1 Journal of Dynamical Systems and Geometric Theories 1 Mediterranean Journal of Mathematics 1 Journal of Industrial and Management Optimization 1 Communications in Mathematical Analysis 1 Optimization Letters 1 Journal of Mathematical Inequalities 1 Discrete and Continuous Dynamical Systems. Series S 1 Journal of Nonlinear Science and Applications 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Analysis and Mathematical Physics 1 Mathematical Control and Related Fields 1 Journal of Applied Analysis and Computation 1 Journal of Function Spaces 1 Nonlinear Analysis. Theory, Methods & Applications 1 Mechanics of Solids
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#### Cited in 29 Fields

 122 Ordinary differential equations (34-XX) 102 Difference and functional equations (39-XX) 58 Dynamical systems and ergodic theory (37-XX) 57 Calculus of variations and optimal control; optimization (49-XX) 40 Systems theory; control (93-XX) 19 Real functions (26-XX) 18 Operations research, mathematical programming (90-XX) 12 Operator theory (47-XX) 11 Mechanics of particles and systems (70-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 7 Partial differential equations (35-XX) 5 Numerical analysis (65-XX) 4 Mechanics of deformable solids (74-XX) 3 Integral equations (45-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Computer science (68-XX) 2 Quantum theory (81-XX) 2 Biology and other natural sciences (92-XX) 1 Topological groups, Lie groups (22-XX) 1 Approximations and expansions (41-XX) 1 Functional analysis (46-XX) 1 Differential geometry (53-XX) 1 Probability theory and stochastic processes (60-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 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX)