Minimal principal solution at infinity for nonoscillatory linear Hamiltonian systems
| Authors | |
|---|---|
| Year of publication | 2014 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Dynamics and Differential Equations |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1007/s10884-013-9342-1 |
| Field | General mathematics |
| Keywords | Linear Hamiltonian system; Minimal principal solution; Principal solution; Controllability; Normality; Conjoined basis; Order of abnormality; Moore--Penrose pseudoinverse |
| Attached files | |
| Description | In this paper we open a new direction in the study of principal solutions for nonoscillatory linear Hamiltonian systems. In the absence of the controllability assumption, we introduce the minimal principal solution at infinity, which is a generalization of the classical principal solution (sometimes called the recessive solution) for controllable systems introduced by W.T.Reid, P.Hartman, and/or W.A.Coppel. The term ``minimal'' refers to the rank of the solution. We show that the minimal principal solution is unique (up to a right nonsingular multiple) and state its basic properties. We also illustrate our new theory by several examples. |
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