Applications of time scale symplectic systems without normality

DOI10.1016/j.jmaa.2007.07.077zbMath1145.39006OpenAlexW2054872683MaRDI QIDQ2467781

Vera Zeidan, Roman Šimon Hilscher

Publication date: 28 January 2008

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2007.07.077

zbMATH Keywords

linear Hamiltonian systempositivityquadratic functionalRiccati matrix equationtime scalenonnegativityconjoined basistime scale symplectic system

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Discrete version of topics in analysis (39A12)

Related Items

Limit point and limit circle classification for symplectic systems on time scales ⋮ Oscillation and spectral theory for linear Hamiltonian systems with nonlinear dependence on the spectral parameter ⋮ Extremal solutions at infinity for symplectic systems on time scales I – Genera of conjoined bases ⋮ Nabla time scale symplectic systems and related quadratic functionals ⋮ Extremal solutions at infinity for symplectic systems on time scales II - Existence theory and limit properties ⋮ Oscillation theorems and Rayleigh principle for linear Hamiltonian and symplectic systems with general boundary conditions ⋮ Symmetric three-term recurrence equations and their symplectic structure ⋮ Sturmian theory for linear Hamiltonian systems without controllability ⋮ Riccati equations for linear Hamiltonian systems without controllability condition ⋮ Riccati equations for abnormal time scale quadratic functionals ⋮ Weyl-Titchmarsh theory for time scale symplectic systems on half line ⋮ Eigenvalue theory for time scale symplectic systems depending nonlinearly on spectral parameter ⋮ Time scale embedding theorem and coercivity of quadratic functionals ⋮ Principal solutions at infinity for time scale symplectic systems without controllability condition ⋮ Comparison theorems for conjoined bases of linear Hamiltonian differential systems and the comparative index ⋮ Transformation preserving controllability for nonlinear optimal control problems with joint boundary conditions ⋮ Local minimality properties of circular motions in \(1/r^\alpha\) potentials and of the figure-eight solution of the 3-body problem ⋮ Picone type identities and definiteness of quadratic functionals on time scales

Cites Work

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• Symplectic difference systems: Variable stepsize discretization and discrete quadratic functionals
• Linear Hamiltonian difference systems: Disconjugacy and Jacobi-type conditions
• Riccati inequality and other results for discrete symplectic systems
• Disconjugacy, transformations and quadratic functionals for symplectic dynamic systems on time scales
• Discrete Sturmian theory
• Discrete Oscillation
• DEFINITENESS OF QUADRATIC FUNCTIONALS
• Monotoneity Properties of Solutions of Hermitian Riccati Matrix Differential Equations
• Reid roundabout theorem for symplectic dynamic systems on time scales

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