RT info:eu-repo/semantics/article
T1 Non-Atkinson perturbations of nonautonomous linear Hamiltonian systems: exponential dichotomy and nonoscillation
A1 Núñez Jiménez, María del Carmen
A1 Obaya, Rafael
AB 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 $M^+$ arefundamental to guarantee the solvability of classical minimization problems given by linear-quadratic control processes.
SN 1040-7294
YR 2017
FD 2017
LK http://uvadoc.uva.es/handle/10324/40498
UL http://uvadoc.uva.es/handle/10324/40498
LA eng
NO Journal of Dunamics and Differential Equations (first online), https://doi.org/10.1007/s10884-017-9637-8
NO Producción Científica
DS UVaDOC
RD 24-nov-2024