Peter Šepitka
Masaryk University
24 Papers
61 Citations
Peter Šepitka is an academic researcher from Masaryk University. The author has contributed to research in topics: Hamiltonian system & Rank (linear algebra). The author has an hindex of 8, co-authored 20 publications.
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Papers
Principal and antiprincipal solutions at infinity of linear Hamiltonian systems
TL;DR: The concept of antiprincipal solutions at infinity was introduced in this article for controllable linear Hamiltonian systems and a generalization of the classical result of W.T. Reid, P. Hartman, or W.A. Coppel was introduced.
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Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems
TL;DR: In this article, a new concept of a multiplicity of a focal point at infinity for conjoined bases was introduced, and a singular Sturmian separation theorem for nonoscillatory linear Hamiltonian systems on an unbounded interval was proved.
15
Focal points and principal solutions of linear Hamiltonian systems revisited
TL;DR: In this article, a unified theory of principal (and antiprincipal) solutions at a finite point and at infinity is presented to obtain new representation of the multiplicities of right and left proper focal points of conjoined bases.
13
Recessive solutions for nonoscillatory discrete symplectic systems
TL;DR: In this article, the existence of a recessive solution is equivalent to the nonoscillation of the system and that recessive solutions can have any rank between explicitly given lower and upper bounds.
12
Singular Sturmian comparison theorems for linear Hamiltonian systems
TL;DR: In this article, the authors prove singular comparison theorems on unbounded intervals for two nonoscillatory linear Hamiltonian systems satisfying the Sturmian majorant condition and the Legendre condition.
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