Por favor, use este identificador para citar o enlazar este ítem:http://uvadoc.uva.es/handle/10324/40498
Título
Non-Atkinson perturbations of nonautonomous linear Hamiltonian systems: exponential dichotomy and nonoscillation
Año del Documento
2017
Descripción
Producción Científica
Documento Fuente
Journal of Dunamics and Differential Equations (first online), https://doi.org/10.1007/s10884-017-9637-8
Zusammenfassung
We analyze the presence of exponential dichotomy (ED) and of global existence of Weyl functions $M^\pm$ for one-parametric families of finite-dimensional nonautonomous linear Hamiltonian systems defined along the orbits of a compact metric space, which are perturbed from an initial one in a direction which does not satisfy the classical Atkinson condition: either they do not have ED for any value of the parameter; or they have it for at least all the nonreal values, in which case the Weyl functions exist and are Herglotz. When the parameter varies in the real line, and if the unperturbed family satisfies the properties of exponential dichotomy and global existence of $M^+$, then these two properties persist in a neighborhood of 0 which agrees either with the whole real line or with an open negative half-line; and in this last case, the ED fails at the right end value. The properties of ED and of global existence of $M^+$ are
fundamental to guarantee the solvability of classical minimization problems given by linear-quadratic control processes.
ISSN
1040-7294
Revisión por pares
SI
Patrocinador
MINECO/FEDER, MTM2015-66330-P
European Commission, H2020-MSCA-ITN-2014
European Commission, H2020-MSCA-ITN-2014
Idioma
eng
Tipo de versión
info:eu-repo/semantics/draft
Derechos
openAccess
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