Calculation of eigenvalues in a nonlinear spectral problem for the Hamiltonian systems of ordinary differential equations

2007 ◽  
Vol 47 (1) ◽  
pp. 171-171
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Spectral Problem ◽  
Hamiltonian Systems ◽  
Nonlinear Spectral Problem

scholarly journals New Neumann System Associated with a 3 × 3 Matrix Spectral Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Fang Li ◽  
Liping Lu
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Spectral Problem ◽  
Hamiltonian Systems ◽  
Lax Pair ◽  
Completely Integrable ◽  
Neumann System ◽  
Matrix Spectral Problem

The nonlinearization approach of Lax pair is applied to the case of the Neumann constraint associated with a 3 × 3 matrix spectral problem, from which a new Neumann system is deduced and proved to be completely integrable in the Liouville sense. As an application, solutions of the first nontrivial equation related to the 3 × 3 matrix spectral problem are decomposed into solving two compatible Hamiltonian systems of ordinary differential equations.

The HELP inequality for lim-p Hamiltonian systems

2000 ◽  
Vol 130 (4) ◽  
pp. 699-720 ◽  
Author(s):  
B. M. Brown ◽  
M. Marletta
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Hamiltonian Systems ◽  
Wide Class ◽  
Limit Point ◽  
Type Singularity ◽  
Linear Hamiltonian Systems ◽  
Infinite Intervals ◽  
Point Type

In a recent paper, Brown, Evans and Marletta extended the HardyEverittLittlewoodPolya inequality from 2nth-order formally self-adjoint ordinary differential equations to a wide class of linear Hamiltonian systems in 2n variables. The paper considered only problems on semi-infinite intervals [a, ∞) with a limit-point type singularity at infinity. In this paper we extend the theory to cover all types of endpoint ( lim-p for n ≤ p ≤ 2n ).

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