Titchmarsh's λ-dependent boundary conditions for Hamiltonian systems

1982 ◽  
pp. 298-317 ◽  
Author(s):  
Don Hinton ◽  
Ken Shaw
Keyword(s):  
Boundary Conditions ◽  
Hamiltonian Systems

scholarly journals The Oscillation Numbers and the Abramov Method of Spectral Counting for Linear Hamiltonian Systems

2021 ◽  
Vol 248 ◽  
pp. 01002
Author(s):  
Julia Elyseeva
Keyword(s):  
Boundary Conditions ◽  
Hamiltonian Systems ◽  
Spectral Parameter ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Spectral Counting ◽  
Hamiltonian Problems ◽  
Differential Systems ◽  
Linear Hamiltonian Systems ◽  
Strict Normality

In this paper we consider linear Hamiltonian differential systems which depend in general nonlinearly on the spectral parameter and with Dirichlet boundary conditions. For the Hamiltonian problems we do not assume any controllability and strict normality assumptions which guarantee that the classical eigenvalues of the problems are isolated. We also omit the Legendre condition for their Hamiltonians. We show that the Abramov method of spectral counting can be modified for the more general case of finite eigenvalues of the Hamiltonian problems and then the constructive ideas of the Abramov method can be used for stable calculations of the oscillation numbers and finite eigenvalues of the Hamiltonian problems.

Eigenvalues and Pole Functions of Hamiltonian Systems with Eigenvalue Depending Boundary Conditions

1993 ◽  
Vol 161 (1) ◽  
pp. 107-154 ◽  
Author(s):  
Aad Dijksma ◽  
Heinz Langer ◽  
Henk de Snoo
Keyword(s):  
Boundary Conditions ◽  
Hamiltonian Systems

scholarly journals J-Self-Adjoint Extensions for a Class of Discrete Linear Hamiltonian Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-19
Author(s):  
Guojing Ren ◽  
Huaqing Sun
Keyword(s):  
Boundary Conditions ◽  
Hamiltonian Systems ◽  
Limit Point ◽  
Limit Circle ◽  
Linear Hamiltonian Systems ◽  
Infinite Intervals ◽  
Defect Indices

This paper is concerned with formallyJ-self-adjoint discrete linear Hamiltonian systems on finite or infinite intervals. The minimal and maximal subspaces are characterized, and the defect indices of the minimal subspaces are discussed. All theJ-self-adjoint subspace extensions of the minimal subspace are completely characterized in terms of the square summable solutions and boundary conditions. As a consequence, characterizations of all theJ-self-adjoint subspace extensions are given in the limit point and limit circle cases.

scholarly journals A NEW VARIATIONAL FORMULATION FOR CONVEX HAMILTONIAN SYSTEMS WITH NONLINEAR BOUNDARY CONDITIONS

2011 ◽  
Vol 84 (2) ◽  
pp. 186-204 ◽  
Author(s):  
MARK LEWIS ◽  
ABBAS MOAMENI
Keyword(s):  
Variational Principle ◽  
Boundary Conditions ◽  
Hamiltonian Systems ◽  
Variational Formulation ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Existence Results ◽  
Second Order ◽  
Second Order Hamiltonian Systems ◽  
New Formulation

AbstractA variational principle is established to provide a new formulation for convex Hamiltonian systems. Using this formulation, we obtain some existence results for second-order Hamiltonian systems with a variety of boundary conditions, including nonlinear ones.

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