Rayleigh principle for linear Hamiltonian systems without controllability

DOI10.1051/cocv/2011104zbMath1254.34120OpenAlexW2091352057MaRDI QIDQ2911445

Werner Kratz, Roman Šimon Hilscher

Publication date: 31 August 2012

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/221899

zbMATH Keywords

normalitylinear Hamiltonian systemquadratic functionaloscillation theoremproper focal pointconjoined basisRayleigh principlefinite eigenvalueself-adjoint eigenvalue problem

Mathematics Subject Classification ID

General spectral theory of ordinary differential operators (34L05) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Boundary eigenvalue problems for ordinary differential equations (34B09)

Related Items

Sturm-Liouville matrix differential systems with singular leading coefficient ⋮ Comparative index and Sturmian theory for linear Hamiltonian systems ⋮ Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter ⋮ Singular Sturmian comparison theorems for linear Hamiltonian systems ⋮ Relative oscillation theory for linear Hamiltonian systems with nonlinear dependence on the spectral parameter ⋮ Reid’s Construction of Minimal Principal Solution at Infinity for Linear Hamiltonian Systems ⋮ Generalized focal points and local Sturmian theory for linear Hamiltonian systems ⋮ Oscillation numbers for continuous Lagrangian paths and Maslov index ⋮ Solutions with prescribed numbers of focal points of nonoscillatory linear Hamiltonian systems ⋮ Comparison theorems for conjoined bases of linear Hamiltonian systems without monotonicity ⋮ Focal points and principal solutions of linear Hamiltonian systems revisited ⋮ Oscillation theorems and Rayleigh principle for linear Hamiltonian and symplectic systems with general boundary conditions ⋮ Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems ⋮ On symplectic transformations of linear Hamiltonian differential systems without normality ⋮ Comparison theorems for self‐adjoint linear Hamiltonian eigenvalue problems ⋮ On the class of canonical systems corresponding to matrix string equations: general-type and explicit fundamental solutions and Weyl-Titchmarsh theory ⋮ Genera of conjoined bases of linear Hamiltonian systems and limit characterization of principal solutions at infinity ⋮ Principal and antiprincipal solutions at infinity of linear Hamiltonian systems ⋮ Sturmian comparison theorems for completely controllable linear Hamiltonian systems in singular case ⋮ The comparative index and transformations of linear Hamiltonian differential systems ⋮ Weak disconjugacy, weak controllability, and genera of conjoined bases for linear Hamiltonian systems ⋮ Principal solutions at infinity of given ranks for nonoscillatory linear Hamiltonian systems

Cites Work

• Nabla time scale symplectic systems and related quadratic functionals
• Picone type identities and definiteness of quadratic functionals on time scales
• Sturmian theory for ordinary differential equations
• Eigenvalue and oscillation theorems for time scale symplectic systems
• Riccati equations for abnormal time scale quadratic functionals
• Sturmian and spectral theory for discrete symplectic systems
• DEFINITENESS OF QUADRATIC FUNCTIONALS
• An Oscillation Theorem for Self-Adjoint Differential Systems and the Rayleigh Principle for Quadratic Functionals
• Oscillation theorems for symplectic difference systems
• Unnamed Item
• Unnamed Item
• Unnamed Item