Minimal principal solution at infinity for nonoscillatory linear Hamiltonian systems

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Authors

ŠEPITKA Peter ŠIMON HILSCHER Roman

Year of publication 2014
Type Article in Periodical
Magazine / Source Journal of Dynamics and Differential Equations
MU Faculty or unit

Faculty of Science

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
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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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