Stability of deficiency indices for discrete Hamiltonian systems under bounded perturbations

Advances in Difference Equations

article

Liu, Yan¹  Xu, Meiru² 

[1] College of Science, Hohai University;Department of Mathematics and Physics, Shandong College of Traditional Chinese Medicine

关键词: Discrete Hamiltonian systems;    Deficiency index;    Perturbation;    Stability;    Hermitian relation;   

DOI  :  10.1186/s13662-020-03084-z

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

This paper is concerned with stability of deficiency indices for discrete Hamiltonian systems under perturbations. By applying the perturbation theory of Hermitian linear relations we establish the invariance of deficiency indices for discrete Hamiltonian systems under bounded perturbations. As a consequence, we obtain the invariance of limit types for the systems under bounded perturbations. In particular, we build several criteria of the invariance of the limit circle and limit point cases for the systems. Some of these results improve and extend some previous results.

【 授权许可】

CC BY