Principal solutions of positive linear Hamiltonian systems

Content Provider	Scilit
Author	Hinton, Don
Copyright Year	1976
Description	The Hamiltonian system Y′ = BY + CZ, Z′ = – AY – B*Z is considered where the coefficients are continuous on I = [a, ∞, C = C* ≧ 0, and A = A* ≦ 0. A solution (Y, Z) satisfying Y*Z = Z*Y is defined to be principal (coprincipal) provided that (i) $Y^{−1}$ exists on I $(Z^{−1}$ exists on I) and (ii) as t→∞ ( as t → ∞). Three conditions are given which are separtely equivalent to the condition that a solution is principal iff it is coprincipal. For a self-adjoint scalar operator L of order $2_{n}$, this problem is related to the deficiency index problem and to a problem of Anderson and Lazer (1970) which concerns the number of lnearly independent solutions of L (y) =0 satisfying $y^{(k)}$ ∈ (a, ∞) (k = 0, …, n).
Related Links	https://www.cambridge.org/core/services/aop-cambridge-core/content/view/09E9A76B475D2F5208494744166C12D8/S1446788700016268a.pdf/div-class-title-principal-solutions-of-positive-linear-hamiltonian-systems-div.pdf
Ending Page	420
Page Count	10
Starting Page	411
ISSN	14467887
e-ISSN	14468107
DOI	10.1017/s1446788700016268
Journal	Journal of the Australian Mathematical Society
Issue Number	4
Volume Number	22
Language	English
Publisher	Cambridge University Press (CUP)
Publisher Date	1976-12-01
Access Restriction	Open
Subject Keyword	Journal of the Australian Mathematical Society Applied Mathematics Hamiltonian System
Content Type	Text
Resource Type	Article
Subject	Mathematics