Limit point, strong limit point and Dirichlet conditions for Hamiltonian differential systems

2011 ◽  
Vol 284 (5-6) ◽  
pp. 764-780 ◽  
Author(s):  
Jiangang Qi ◽  
Hongyou Wu
Keyword(s):  
Limit Point ◽  
Strong Limit ◽  
Differential Systems ◽  
Dirichlet Conditions

Strong limit-point and Dirichlet criteria for ordinary differential expressions of order 2n

1977 ◽  
Vol 76 (4) ◽  
pp. 301-310 ◽  
Author(s):  
Don Hinton
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Limit Point ◽  
Half Line ◽  
Integral Type ◽  
Strong Limit ◽  
Order Ordinary Differential Equation ◽  
Dirichlet Conditions

SynopsisConditions are given which ensure that a weighted 2nth order ordinary differential equation on a half-line satisfy the strong limit-point and Dirichlet conditions. Perturbation terms are permitted which either satisfy certain pointwise bounds or integral type bounds. Not all of the coefficients of the equation are required to be non-negative.

HELP inequalities for limit-circle and regular problems

1991 ◽  
Vol 432 (1886) ◽  
pp. 367-390 ◽  
Keyword(s):  
Differential Equation ◽  
Limit Point ◽  
Strong Limit ◽  
End Points ◽  
Limit Circle ◽  
End Point ◽  
Limit Circle Case ◽  
Limit Point Case ◽  
Regular Problems ◽  
Circle Case

Everitt’s criterion for the validity of the generalized Hardy-Littlewood inequality presupposes that the associated differential equation is singular at one end-point of the interval of definition and is in the strong-limit-point case at the end-point. In this paper we investigate the cases when the differential equation is in the limit-circle case and non-oscillatory at the singular end-point and when both end-points of the interval are regular.

On a strong limit-point condition and an integral inequality associated with a symmetric matrix differential expression

1977 ◽  
Vol 76 (2) ◽  
pp. 155-159 ◽  
Author(s):  
D. A. R. Rigler
Keyword(s):  
Differential Expression ◽  
Vector Function ◽  
Real Line ◽  
Integral Inequality ◽  
Limit Point ◽  
Symmetric Matrix ◽  
Strong Limit ◽  
The Matrix ◽  
Point Condition ◽  
Matrix Differential

SynopsisThis paper is concerned with some properties of an ordinary symmetric matrix differential expression M, denned on a certain class of vector-functions, each of which is defined on the real line. For such a vector-function F we have M[F] = −F“ + QF on R, where Q is an n × n matrix whose elements are reasonably behaved on R. M is classified in an equivalent of the limit-point condition at the singular points ± ∞, and conditions on the matrix coefficient Q are given which place M, when n> 1, in the equivalent of the strong limit-point for the case n = 1. It is also shown that the same condition on Q establishes the integral inequality for a certain class of vector-functions F.

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