# Publications of Roman Simon Hilscher

Click on the title for the abstract.

MathSciNet, Zentralblatt Math, ResearcherID, ORCID, Scopus, Web of Science, Mendeley

 117 (with J. Elyseeva and P. Sepitka) Oscillation numbers for continuous Lagrangian paths and Maslov index, J. Dynam. Differential Equations, in press (2022), doi: 10.1007/s10884-022-10140-7. 116 (with P. Sepitka) Weak disconjugacy, weak controllability, and genera of conjoined bases for linear Hamiltonian systems, Ann. Mat. Pura Appl. (4), in press (2022), doi: 10.1007/s10231-022-01194-x. 115 (with P. Sepitka) Lidskii angles and Sturmian theory for linear Hamiltonian systems on compact interval, J. Differential Equations 298 (2021), 1-29. 114 (with V. Zeidan) Transformation preserving controllability for nonlinear optimal control problems with joint boundary conditions, ESAIM Control Optim. Calc. Var. 27 (2021), Paper No. 75, 35 pp. 113 (with P. Sepitka) Comparative index and Lidskii angles for symplectic matrices, Linear Algebra Appl. 624 (2021), 174-197. 112 (with P. Sepitka) Distribution and number of focal points for linear Hamiltonian systems, Linear Algebra Appl. 611 (2021), 26-45. 111 (with I. Drimalova) Antiprincipal solutions at infinity for symplectic systems on time scales, Electron. J. Qual. Theory Differ. Equ. 2020 (2020), no. 44, 32 pp. (electronic). 110 (with P. Sepitka) Sturmian comparison theorems for completely controllable linear Hamiltonian systems in singular case, J. Math. Anal. Appl. 487 (2020), no. 2, Art. 124030, 14 pp. 109 (with P. Sepitka) Singular Sturmian comparison theorems for linear Hamiltonian systems, J. Differential Equations 269 (2020), no. 4, 2920-2955. 108 (with O. Dosly and J. Elyseeva) Symplectic Difference Systems: Oscillation and Spectral Theory, Pathways in Mathematics, Birkhauser/Springer, Cham, 2019. 107 (with P. Sepitka) Singular Sturmian separation theorems for nonoscillatory symplectic difference systems, J. Difference Equ. Appl. 24 (2018), no. 12, 1894-1934. 106 (with P. Sepitka) Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems, J. Differential Equations 266 (2019), no. 11, 7481--7524. 105 (with J .Elyseeva) Discrete oscillation theorems for symplectic eigenvalue problems with general boundary conditions depending nonlinearly on spectral parameter, Linear Algebra Appl. 558 (2018), 108-145. 104 (with P. Sepitka) Focal points and principal solutions of linear Hamiltonian systems revisited, J. Differential Equations 264 (2018), no. 9, 5541-5576. 103 (with V. Zeidan) Sufficiency and sensitivity for nonlinear optimal control problems on time scales via coercivity, ESAIM Control Optim. Calc. Var. 24 (2018), no. 4, 1705--1734. 102 (with P. Zemanek) On square integrable solutions and principal and antiprincipal solutions for linear Hamiltonian systems, Ann. Mat. Pura Appl. (4) 197 (2018), no. 1, 283-306. 101 (with P. Sepitka) Dominant and recessive solutions at infinity and genera of conjoined bases for discrete symplectic systems, J. Difference Equ. Appl. 23 (2017), no. 4, 657-698. 100 (with P. Sepitka) Comparative index and Sturmian theory for linear Hamiltonian systems, J. Differential Equations 262 (2017), no. 2, 914-944. 99 (with I. Drimalova and W. Kratz) Sturm-Liouville matrix differential systems with singular leading coefficient, Ann. Mat. Pura Appl. (4) 196 (2017), no. 3, 1165-1183. 98 (with P. Sepitka) Principal solutions at infinity for time scale symplectic systems without controllability condition, J. Math. Anal. Appl. 444 (2016), no. 2, 852-880. 97 (with P. Sepitka) Genera of conjoined bases of linear Hamiltonian systems and limit characterization of principal solutions at infinity, J. Differential Equations 260 (2016), no. 8, 6581-6603. 96 (with P. Sepitka) Reid's construction of minimal principal solution at infinity for linear Hamiltonian systems, in: ``Differential and Difference Equations with Applications'', Proceedings of the International Conference on Differential & Difference Equations and Applications (Amadora, 2015), S. Pinelas, Z. Dosla, O. Dosly, and P. E. Kloeden, editors, Springer Proceedings in Mathematics & Statistics, Vol. 164, pp. 359-369, Springer, Berlin, 2016. 95 Eigenvalue comparison for discrete symplectic systems, in: ``Difference Equations, Discrete Dynamical Systems and Applications'', Proceedings of the 20th International Conference on Difference Equations and Applications (Wuhan, 2014), M. Bohner, Y. Ding, and O. Dosly, editors, Springer Proceedings in Mathematics & Statistics, Vol. 150, pp. 95-107, Springer, Berlin, 2015. 94 Asymptotic properties of solutions of Riccati matrix equations and inequalities for discrete symplectic systems, Electron. J. Qual. Theory Differ. Equ. 2015 (2015), no. 54, 16 pp. (electronic). 93 (with P. Sepitka) Principal and antiprincipal solutions at infinity of linear Hamiltonian systems, J. Differential Equations 259 (2015), no. 9, 4651-4682. 92 (with P. Zemanek) Time scale symplectic systems with analytic dependence on spectral parameter, J. Difference Equ. Appl. 21 (2015), no. 3, 209-239. 91 (with P. Sepitka) Recessive solutions for nonoscillatory discrete symplectic systems, Linear Algebra Appl. 469 (2015), 243-275. 90 (with P. Zemanek) Limit circle invariance for two differential systems on time scales, Math. Nachr. 288 (2015), no. 5-6, 696-709. 89 (with P. Sepitka) Principal solutions at infinity of given ranks for nonoscillatory linear Hamiltonian systems, J. Dynam. Differential Equations 27 (2015), no. 1, 137-175. 88 (with P. Zemanek) Generalized Lagrange identity for discrete symplectic systems and applications in Weyl-Titchmarsh theory, in: ``Theory and Applications of Difference Equations and Discrete Dynamical Systems'', Proceedings of the 19th International Conference on Difference Equations and Applications (Muscat, 2013), Z. AlSharawi, J. Cushing, and S. Elaydi, editors, Springer Proceedings in Mathematics & Statistics, Vol. 102, pp. 187-202, Springer, Berlin, 2014. 87 (with P. Zemanek) Limit point and limit circle classification for symplectic systems on time scales, Appl. Math. Comput. 233 (2014), 623-646. 86 (with P. Sepitka) Minimal principal solution at infinity for nonoscillatory linear Hamiltonian systems, J. Dynam. Differential Equations 26 (2014), no. 1, 57-91. 85 (with P. Zemanek) Weyl disks and square summable solutions for discrete symplectic systems with jointly varying endpoints, Adv. Difference Equ. 2013 (2013), no. 232, 18 pp. 84 Comparison theorems for self-adjoint linear Hamiltonian eigenvalue problems, Math. Nachr. 287 (2014), no. 5-6, 704-716. 83 (with P. Zemanek) Weyl-Titchmarsh theory for discrete symplectic systems with general linear dependence on spectral parameter, J. Difference Equ. Appl. 20 (2014), no. 1, 84-117. 82 Oscillation and spectral theory of Sturm-Liouville differential equations with nonlinear dependence in spectral parameter, Dynam. Systems Appl. 22 (2013), no. 1, 115-124. 81 (with W. Kratz) A generalized index theorem for monotone matrix-valued functions with applications to discrete oscillation theory, SIAM J. Matrix Anal. Appl. 34 (2013), no. 1, 228-243. 80 Eigenvalue theory for time scale symplectic systems depending nonlinearly on spectral parameter, Appl. Math. Comput. 219 (2012), no. 6, 2839-2860. 79 Spectral and oscillation theory for general second order Sturm-Liouville difference equations, in: ``Oscillation of Difference, Differential, and Dynamic Equations'', M. Bohner, Z. Dosla, and S. Pinelas, editors, Adv. Difference Equ. 2012 (2012), no. 82, 19 pp. 78 Oscillation theorems for discrete symplectic systems with nonlinear dependence in spectral parameter, Linear Algebra Appl. 437 (2012), no. 12, 2922-2960. 77 (with O. Dosly and A. Ozbekler) Oscillation criterion for half-linear differential equations with periodic coefficients, J. Math. Anal. Appl. 393 (2012), no. 2, 360-366. 76 (with V. Zeidan) Oscillation theorems and Rayleigh principle for linear Hamiltonian and symplectic systems with general boundary conditions, Appl. Math. Comput. 218 (2012), no. 17, 8309-8328. 75 (with P. Zemanek) New results for time reversed symplectic dynamic systems and quadratic functionals, The 9th Colloquium on the Qualitative Theory of Differential Equations, No. 15, 11 pp. (electronic), Proc. Colloq. Qual. Theory Differ. Equ., Vol. 9, Electron. J. Qual. Theory Differ. Equ., Bolyai Inst., Univ. Szeged, Szeged, 2012. 74 (with V. Zeidan) Rayleigh principle for time scale symplectic systems and applications, Electron. J. Qual. Theory Differ. Equ. 2011 (2011), no. 83, 26 pp. (electronic). 73 (with M. Bohner and W. Kratz) Oscillation and spectral theory for linear Hamiltonian systems with nonlinear dependence on the spectral parameter, Math. Nachr. 285 (2012), no. 11-12, 1343-1356. 72 (with V. Zeidan) Hamilton-Jacobi theory over time scales and applications to linear-quadratic problems, Nonlinear Anal. 75 (2012), no. 2, 932-950. 71 (with P. Zemanek) Overview of Weyl-Titchmarsh theory for second order Sturm-Liouville equations on time scales, Int. J. Difference Equ. 6 (2011), no. 1, 39-51. 70 (with V. Zeidan) First order conditions for generalized variational problems over time scales, Comput. Math. Appl. 62 (2011), no. 9, 3490-3503. 69 (with P. Zemanek) Weyl-Titchmarsh theory for time scale symplectic systems on half line, in: ``Recent Progress in Differential and Difference Equations'', Proceedings of the Conference on Differential and Difference Equations and Applications (Rajecke Teplice, 2010), J. Diblik, E. Braverman, Y. Rogovchenko, and M. Ruzickova, editors, Abstr. Appl. Anal. 2011 (2011), Art. ID 738520, 41 pp. 68 On general Sturmian theory for abnormal linear Hamiltonian systems, in: ``Dynamical Systems, Differential Equations and Applications'', Proceedings of the 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications'' (Dresden, 2010), W. Feng, Z. Feng, M. Grasselli, A. Ibragimov, X. Lu, S. Siegmund, and J. Voigt, editors, Discrete Contin. Dynam. Systems, Suppl. 2011, pp. 684-691, American Institute of Mathematical Sciences (AIMS), Springfield, MO, 2011. 67 Sturmian theory for linear Hamiltonian systems without controllability, Math. Nachr. 284 (2011), no. 7, 831-843. 66 (with V. Zeidan) Symmetric three-term recurrence equations and their symplectic structure, Adv. Difference Equ. 2010 (2010), Art. ID 626942, 17 pp. 65 (with W. Kratz) Rayleigh principle for linear Hamiltonian systems without controllability, ESAIM Control Optim. Calc. Var. 18 (2012), no. 2, 501-519. 64 (with P. Zemanek) Friedrichs extension of operators defined by linear Hamiltonian systems on unbounded interval, in: ``Equadiff 12'', Proceedings of the International Conference on Differential Equations and Their Applications (Brno, 2009), J. Diblik, O. Dosly, P. Drabek, and E. Feistauer, editors, Math. Bohem. 135 (2010), no. 2, 209-222. 63 (with V. Zeidan) Symplectic structure of Jacobi systems on time scales, Int. J. Difference Equ. 5 (2010), no. 1, 55-81. 62 (with W. Kratz and V. Zeidan) Eigenvalue and oscillation theorems for time scale symplectic systems, in: ``Dynamic Equations on Time Scales and Applications'', L.Erbe and A.Peterson, editors, Int. J. Dyn. Syst. Differ. Equ. 3 (2011), no. 1-2, 84-131. 61 (with V. Zeidan) Picone type identities and definiteness of quadratic functionals on time scales, Appl. Math. Comput. 215 (2009), no. 7, 2425-2437. 60 A note on the time scale calculus of variations problems, in: ``Ulmer Seminare uber Funktionalanalysis und Differentialgleichungen'', Vol. 14, pp. 223-230, University of Ulm, Ulm, 2009. 59 (with P. Zemanek) Definiteness of quadratic functionals for Hamiltonian and symplectic systems: A survey, Int. J. Difference Equ. 4 (2009), no. 1, 49-67. 58 (with V. Zeidan) Oscillation results for time scale symplectic systems, in: ``Proceedings of the 14th International Conference on Difference Equations and Applications'' (Istanbul, 2008), M. Bohner, Z. Dosla, G. Ladas, M. Unal, and A. Zafer, editors, pp. 203-210, Ugur-Bahcesehir University Publishing Company, Istanbul, 2009. 57 (with W. Kratz and V. Zeidan) Differentiation of solutions of dynamic equations on time scales with respect to parameters, Adv. Dyn. Syst. Appl. 4 (2009), no. 1, 35-54. 56 (with V. Zeidan) Nabla time scale symplectic systems and related quadratic functionals, Differ. Equ. Dyn. Syst. 18 (2010), no. 1-2, 163-198. 55 Optimality Conditions for Time Scale Variational Problems, DSc dissertation, Masaryk University, Brno, 2008. 54 (with P. Zemanek) Trigonometric and hyperbolic systems on time scales, Dynam. Systems Appl. 18 (2009), no. 3-4, 483-506. 53 (with C. C. Tisdell) Terminal value problems for first and second order nonlinear equations on time scales, Electron. J. Differential Equations 2008 (2008), no. 68, 1-21. 52 (with V. Zeidan) Multiplicities of focal points for discrete symplectic systems: revisited, J. Difference Equ. Appl. 15 (2009), no. 10, 1001-1010. 51 (with V. Zeidan) Reid roundabout theorems for time scale symplectic systems, in: ``Discrete Dynamics and Difference Equations'', Proceedings of the Twelfth International Conference on Difference Equations and Applications (Lisbon, 2007), S. Elaydi, H. Oliveira, J. M. Ferreira, and J. F. Alves, editors, pp. 267-288, World Scientific Publishing Co., London, 2010. 50 (with V. Zeidan) Weak maximum principle and accessory problem for control problems on time scales, Nonlinear Anal. 70 (2009), no. 9, 3209-3226. 49 (with V. Ruzickova) Perturbation of time scale quadratic functionals with variable endpoints, Adv. Dyn. Syst. Appl. 2 (2007), no. 2, 207-224. 48 (with V. Zeidan) Riccati equations for abnormal time scale quadratic functionals, J. Differential Equations 244 (2008), no. 6, 1410-1447. 47 (with V. Zeidan) Extension of discrete LQR-problem to symplectic systems, Int. J. Difference Equ. 2 (2007), no. 2, 197-208. 46 (with V. Zeidan) Time scale embedding theorem and coercivity of quadratic functionals, Analysis (Munich) 28 (2008), no. 1, 1-28. 45 Comparison results for solutions of time scale matrix Riccati equations and inequalities, Aust. J. Math. Anal. Appl. 3 (2006), no. 2, Article 13, 1-15. 44 (with V. Ruzickova) Implicit Riccati equations and quadratic functionals for discrete symplectic systems, Int. J. Difference Equ. 1 (2006), no. 1, 135-154. 43 (with V. Ruzickova) Perturbation of nonnegative time scale quadratic functionals, in: ``Difference Equations, Special Functions, and Orthogonal Polynomials'', Proceedings of the International Conference (Munich, 2005), S. Elaydi, J. Cushing, R. Lasser, A. Ruffing, V. Papageorgiou, and W. Van Assche, editors, pp. 266-275, World Scientific, London, 2007. 42 (with V. Zeidan) Applications of time scale symplectic systems without normality, J. Math. Anal. Appl. 340 (2008), no. 1, 451-465. 41 (with V. Zeidan) Time scale symplectic systems without normality, J. Differential Equations 230 (2006), no. 1, 140-173. 40 (with V. Ruzickova) Riccati inequality and other results for discrete symplectic systems, J. Math. Anal. Appl. 322 (2006), no. 2, 1083-1098. 39 (with V. Zeidan) Coupled intervals for discrete symplectic systems, Linear Algebra Appl. 419 (2006), no. 2-3, 750-764. 38 (with V. Zeidan) Legendre, Jacobi, and Riccati type conditions for time scale variational problem with application, Dynam. Systems Appl. 16 (2007), no. 3, 451-480. 37 (with V. Zeidan) Calculus of variations on time scales: weak local piecewise $C1$rd solutions with variable endpoints, J. Math. Anal. Appl. 289 (2004), no. 1, 143-166. 36 (with V. Zeidan) Nonnegativity and positivity of quadratic functionals in discrete calculus of variations: Survey, J. Difference Equ. Appl. 11 (2005), no. 9, 857-875. 35 (with M. Bohner, O. Dosly, and W. Kratz) Diagonalization approach to discrete quadratic functionals, Arch. Inequal. Appl. 1 (2003), no. 2, 261-274. 34 (with V. Zeidan) Solvability of the discrete LQR-problem under minimal assumptions, in: ``Difference Equations and Discrete Dynamical Systems'', Proceedings of the Ninth International Conference on Difference Equations and Applications (Los Angeles, 2004), L. Allen, B. Aulbach, S. Elaydi, and R. Sacker, editors, pp. 273-282, World Scientific Publishing Co., London, 2005. 33 (with P. Rehak) Riccati inequality, disconjugacy, and reciprocity principle for linear Hamiltonian dynamic systems, in: ``Dynamic Equations on Time Scales'', M. Bohner and B. Kaymakcalan, editors, Dynam. Systems Appl. 12 (2003), no. 1-2, 171-189. 32 (with O. Dosly and V. Zeidan) Nonnegativity of discrete quadratic functionals corresponding to symplectic difference systems, Linear Algebra Appl. 375 (2003), 21-44. 31 Quadratic Functionals in Discrete Optimal Control, habilitation, Masaryk University, Brno, 2003. 30 (with V. Zeidan) Coupled intervals in the discrete optimal control, J. Difference Equ. Appl. 10 (2004), no. 2, 151-186. 29 (with O. Dosly and S. Hilger) Symplectic dynamic systems, in: `` Advances in Dynamic Equations on Time Scales'', M. Bohner and A. Peterson, editors, pp. 293-334, Birkhauser, Boston, 2003. 28 (with V. Zeidan) Equivalent conditions to the nonnegativity of a quadratic functional in discrete optimal control, Math. Nachr. 266 (2004), 48-59. 27 (with V. Zeidan) Symplectic difference systems: variable stepsize discretization and discrete quadratic functionals, Linear Algebra Appl. 367 (2003), 67-104. 26 (with V. Zeidan) Discrete quadratic functionals with jointly varying endpoints via separable endpoints, in: ``New Progress in Difference Equations'', Proceedings of the Sixth International Conference on Difference Equations (Augsburg, 2001), B. Aulbach, S. Elaydi, and G. Ladas, editors, pp. 461-470, Chapman & Hall/CRC, Boca Raton, FL, 2004. 25 (with M. Bohner) An eigenvalue problem for linear Hamiltonian dynamic systems, Fasc. Math. 35 (2005), 35-49. 24 (with V. Zeidan) A remark on discrete quadratic functionals with separable endpoints, Rocky Mountain J. Math. 33 (2003), no. 4, 1337-1351. 23 (with V. Zeidan) Discrete optimal control: second order optimality conditions, J. Difference Equ. Appl. 8 (2002), no. 10, 875-896. 22 (with V. Zeidan) Coupled intervals in the discrete calculus of variations: necessity and sufficiency, J. Math. Anal. Appl. 276 (2002), no. 1, 396-421. 21 (with V. Zeidan) Nonnegativity of a discrete quadratic functional in terms of the (strengthened) Legendre and Jacobi conditions, in: ``Advances in Difference Equations IV'', R. P. Agarwal, editor, Comput. Math. Appl. 45 (2003), no. 6-9, 1369-1383. 20 (with V. Zeidan) Second order sufficiency criteria for a discrete optimal control problem, J. Difference Equ. Appl. 8 (2002), no. 6, 573-602. 19 (with M. Bohner and O. Dosly) Linear Hamiltonian dynamic systems on time scales: Sturmian property of the principal solution, in: ``Proceedings of the Third World Congress of Nonlinear Analysts'' (Catania, 2000), Nonlinear Anal. 47 (2001), 849-860. 18 A time scales version of a Wirtinger type inequality and applications, in: ``Dynamic Equations on Time Scales'', R. P. Agarwal, M. Bohner, and D. O'Regan, editors, J. Comput. Appl. Math. 141 (2002), no. 1-2, 219-226 17 (with O. Dosly) A class of Sturm-Liouville difference equations: (non)oscillation constants and property BD, in: ``Advances in Difference Equations IV'', R. P. Agarwal, editor, Comput. Math. Appl. 45 (2003), no. 6-9, 961-981. 16 Discrete spectra criteria for certain classes of singular diffferential and difference operators, in: ``Advances in Difference Equations III'', R. P. Agarwal, editor, Comput. Math. Appl. 42 (2001), no. 3-5, 465-476. 15 Reid roundabout theorem for symplectic dynamic systems on time scales, Appl. Math. Optim. 43 (2001), no. 2, 129-146. 14 (with O. Dosly) Disconjugacy, transformations and quadratic functionals for symplectic dynamic systems on time scales, J. Differ. Equations Appl. 7 (2001), 265-295. 13 Positivity of quadratic functionals on time scales: necessity, Math. Nachr. 226 (2001), 85-98. 12 (with V. Zeidan) Discrete optimal control: the accessory problem and necessary optimality conditions, J. Math. Anal. Appl. 243 (2000), no. 2, 429-452. 11 On disconjugacy for vector linear Hamiltonian systems on time scales, in: ``Communications in Difference Equations'', Proceedings of the Fourth International Conference on Difference Equations (Poznan, 1998), S. Elaydi, G. Ladas, J. Popenda, and J. Rakowski, editors, pp. 181-188, Gordon and Breach, Amsterdam, 2000. 10 Linear Hamiltonian systems on time scales: transformations, in: ``Discrete and Continuous Hamiltonian Systems'', R. P. Agarwal and M. Bohner, editors, Dynam. Systems Appl. 8 (1999), no. 3-4, 489-501. 9 Inhomogeneous quadratic functionals on time scales, J. Math. Anal. Appl. 253 (2001), no. 2, 473-481. 8 Linear Hamiltonian systems on time scales: positivity of quadratic functionals, in: ``Boundary value problems and related topics'', A. C. Peterson, editor, Math. Comput. Modelling 32 (2000), no. 5-6, 507-527. 7 Some Aspects of the Qualitative Theory of Linear Hamiltonian Systems, PhD dissertation, Masaryk University, Brno, 1998. 6 A unified approach to continuous and discrete linear Hamiltonian systems via the calculus on time scales (Riccati equation, Picone identity, disconjugacy, transformations and quadratic functionals), research report, University of Ulm, 1997, in: ``Ulmer Seminare uber Funktionalanalysis und Differentialgleichungen'', Vol. 3, pp. 215-249, University of Ulm, Ulm, 1998. 5 (with O. Dosly) Linear Hamiltonian difference systems: transformations, recessive solutions, generalized reciprocity, in: ``Discrete and Continuous Hamiltonian Systems'', R. P. Agarwal and M. Bohner, editors, Dynam. Systems Appl. 8 (1999), no. 3-4, 401-420. 4 Disconjugacy of symplectic systems and positive definiteness of block tridiagonal matrices, Rocky Mountain J. Math. 29 (1999), no. 4, 1301-1319. 3 Spectral properties of general self-adjoint, even order differential operators, Math. Slovaca 50 (2000), no. 2, 165-186. 2 (with O. Dosly), Spectral properties of fourth order differential operators, Math. Bohem. 122 (1997), no. 2, 153-168. 1 Spektralni vlastnosti singularnich diferencialnich operatoru (Czech), [Spectral Properties of Singular Differential Operators], MSc thesis, Masaryk University, Brno, 1995.

Zpatky na hlavni stranu. / Back to the main page.

Last change: 02.03.2022. (c) Roman Simon Hilscher