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 ).

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 Nonlinear Limit-Point Type Solutions ofnth Order Differential Equations

1997 ◽  
Vol 209 (1) ◽  
pp. 122-139 ◽  
Author(s):  
M Bartušek ◽  
Z Došlá ◽  
John R Graef
Keyword(s):  
Differential Equations ◽  
Limit Point ◽  
Point Type

Numerical Solution of the Beam Equation With Nonuniform Foundation Coefficient

1979 ◽  
Vol 46 (4) ◽  
pp. 901-904 ◽  
Author(s):  
M. Lentini
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
New Method ◽  
Beam Equation ◽  
Infinite Intervals

A new method for computing the solutions of the beam equation is given for the case of the problem of a pile. The method could be used for other problems where it is necessary to solve boundary-value problems for ordinary differential equations over semi-infinite intervals.

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