Publication details

Principal solutions at infinity of given ranks for nonoscillatory linear Hamiltonian systems



Year of publication 2015
Type Article in Periodical
Magazine / Source Journal of Dynamics and Differential Equations
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords Linear Hamiltonian system; Principal solution at infinity; Minimal principal solution; Controllability; Normality; Conjoined basis; Order of abnormality; Genus of conjoined bases; Moore-Penrose pseudoinverse
Description In this paper we study the existence and properties of the principal solutions at infinity of nonoscillatory linear Hamiltonian systems without any controllability assumption. As our main results we prove that the principal solutions can be classified according to the rank of their first component and that the principal solutions exist for any rank in the range between explicitly given minimal and maximal values. The minimal rank then corresponds to the minimal principal solution at infinity introduced by the authors in their previous paper, while the maximal rank corresponds to the principal solution at infinity developed by W.T.Reid, P.Hartman or W.A.Coppel. We also derive a classification of the principal solutions, which have eventually the same image. The proofs are based on a detailed analysis of conjoined bases with a given rank and their construction from the minimal conjoined bases. We illustrate our new theory by several examples.
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