Publication details

Reid's construction of minimal principal solution at infinity for linear Hamiltonian systems



Year of publication 2016
Type Article in Proceedings
Conference Differential and Difference Equations with Applications: ICDDEA, Amadora, Portugal, May 2015, Selected Contributions
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords Linear Hamiltonian system; Principal solution at infinity; Antiprincipal solution at infinity; Minimal principal solution at infinity; Controllability; Moore-Penrose pseudoinverse
Description Recently the authors introduced a theory of principal solutions at infinity for nonoscillatory linear Hamiltonian systems in the absence of the complete controllability assumption. In this theory the so-called minimal principal solution at infinity plays a distinguished role (the minimality refers to the rank of the first component of the solution). In this paper we show that the minimal principal solution at infinity can be obtained by a suitable generalization of the Reid construction of the principal solution known in the controllable case. Our new result points to some applications of the minimal principal solution at infinity e.g. in the spectral theory of linear Hamiltonian systems.

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