کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6417188 | 1338534 | 2015 | 32 صفحه PDF | دانلود رایگان |
The concept of principal solutions at infinity for possibly abnormal linear Hamiltonian systems was recently introduced by the authors. In this paper we develop the theory of antiprincipal solutions at infinity and establish a limit characterization of the principal solutions. That is, we prove that the principal solutions are the smallest ones at infinity when they are compared with the antiprincipal solutions. This statement is a generalization of the classical result of W.T. Reid, P. Hartman, or W.A. Coppel for controllable linear Hamiltonian systems. We also derive a classification of antiprincipal solutions at infinity according to their rank and show that the antiprincipal solutions exist for any rank in the range between explicitly given minimal and maximal values. We illustrate our new theory by several examples.
Journal: Journal of Differential Equations - Volume 259, Issue 9, 5 November 2015, Pages 4651-4682