Linear Hamiltonian systems on time scales: transformations

HILSCHER, Roman. Linear Hamiltonian systems on time scales: transformations. Dynamic Systems and Applications. Atlanta, USA: Dynamic Publishers,Inc., 1999, vol. 8, 3-4, p. 489-501, 12 pp. ISSN 1056-2176.

Basic information

• Original name: Linear Hamiltonian systems on time scales: transformations
• Authors: HILSCHER, Roman (203 Czech Republic, guarantor).
• Edition: Dynamic Systems and Applications, Atlanta, USA, Dynamic Publishers,Inc. 1999, 1056-2176.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10101 Pure mathematics
• Country of publisher: United States of America
• Confidentiality degree: is not subject to a state or trade secret
• RIV identification code: RIV/00216224:14310/99:00008158
• Organization unit: Faculty of Science
• Keywords in English: time scale; (continuous and discrete) linear Hamiltonian system; transformation; disconjugacy; principal solution
• Tags: disconjugacy, Principal solution, time scale, transformation

Abstract

In this work we develop a transformation theory for linear Hamiltonian systems on an arbitrary time scale T. We prove that, under suitable assumptions, a linear Hamiltonian system is transformed into a system of the same form, which includes the corresponding continuous (T=R) and discrete (T=Z) results as special cases. Since we allow the matrix B to be singular, the important Sturm-Liouville equations of higher order may be studied as a special linear Hamiltonian system.

Links

• GA201/96/0410, research and development project: Name: Diferenciální a funkcionálně-diferenciální rovnice

Investor: Czech Science Foundation, Differential and functional - differential equations

• GA201/98/0677, research and development project: Name: Diferenční rovnice a jejich aplikace

Investor: Czech Science Foundation, Difference equations and their applications