Weyl-Titchmarsh theory for Hamiltonian dynamic systems.
Sun, Shurong, Bohner, Martin, Chen, Shaozhu (2010)
Abstract and Applied Analysis
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Sun, Shurong, Bohner, Martin, Chen, Shaozhu (2010)
Abstract and Applied Analysis
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Brown, B. M., Evans, W. D., Marletta, M. (1999)
Journal of Inequalities and Applications [electronic only]
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Huang, Xuncheng, Tu, Guizhang (2006)
International Journal of Mathematics and Mathematical Sciences
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Werner Kratz (1998)
Archivum Mathematicum
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In this paper we give a survey on the theory of quadratic functionals. Particularly the relationships between positive definiteness and the asymptotic behaviour of Riccati matrix differential equations, and between the oscillation properties of linear Hamiltonian systems and Rayleigh’s principle are demonstrated. Moreover, the main tools form control theory (as e.g. characterization of strong observability), from the calculus of variations (as e.g. field theory and Picone’s identity),...
Mehrmann, Volker, Xu, Hongguo (2008)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Henryk Żołądek (2011)
Banach Center Publications
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The first and the second Painlevé equations are explicitly Hamiltonian with time dependent Hamilton function. By a natural extension of the phase space one gets corresponding autonomous Hamiltonian systems in ℂ⁴. We prove that the latter systems do not have any additional algebraic first integral. In the proof equations in variations with respect to a parameter are used.
Nutku, Yavuz (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Joanna Janczewska, Jakub Maksymiuk (2012)
Open Mathematics
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We consider a conservative second order Hamiltonian system in ℝ3 with a potential V having a global maximum at the origin and a line l ∩ 0 = ϑ as a set of singular points. Under a certain compactness condition on V at infinity and a strong force condition at singular points we study, by the use of variational methods and geometrical arguments, the existence of homoclinic solutions of the system.
Rodman, Leiba (2008)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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