Picone type identities and definiteness of quadratic functionals on time scales

DOI10.1016/j.amc.2009.08.044zbMath1178.93094OpenAlexW1992832506MaRDI QIDQ1044408

Roman Šimon Hilscher, Vera Zeidan

Publication date: 18 December 2009

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2009.08.044

zbMATH Keywords

controllabilitynormalitylinear Hamiltonian systempositivityquadratic functionaltime scalePicone identitydiscrete symplectic systemnonnegativityconjoined basistime scale symplectic system

Mathematics Subject Classification ID

Controllability (93B05) Time-scale analysis and singular perturbations in control/observation systems (93C70) Control/observation systems governed by ordinary differential equations (93C15)

Related Items

Rayleigh principle for linear Hamiltonian systems without controllability ⋮ Oscillation theorems and Rayleigh principle for linear Hamiltonian and symplectic systems with general boundary conditions ⋮ Eigenvalue theory for time scale symplectic systems depending nonlinearly on spectral parameter ⋮ Principal solutions at infinity of given ranks for nonoscillatory linear Hamiltonian systems

Cites Work

• Time scale symplectic systems without normality
• Weak maximum principle and accessory problem for control problems on time scales
• Disconjugacy and transformations for symplectic systems
• Calculus of variations on time scales: Weak local piecewise \(C_{\text{rd}}^{1}\) solutions with variable endpoints.
• Generalized inverses. Theory and applications.
• Linear Hamiltonian difference systems: Disconjugacy and Jacobi-type conditions
• Eigenvalue and oscillation theorems for time scale symplectic systems
• Applications of time scale symplectic systems without normality
• Riccati equations for abnormal time scale quadratic functionals
• Disconjugacy
• Quadratic functionals for second order matrix equations on time scales
• POSITIVE SEMIDEFINITENESS OF DISCRETE QUADRATIC FUNCTIONALS
• DEFINITENESS OF QUADRATIC FUNCTIONALS
• Time scale embedding theorem and coercivity of quadratic functionals
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