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 ofWeyl functions M± for one-parametric families of finite-dimensional nonautonomous linearHamiltonian systems defined along the orbits of a compact metric space, which are perturbedfrom 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 thenonreal values, in which case theWeyl functions exist and are Herglotz. When the parametervaries in the real line, and if the unperturbed family satisfies the properties of exponentialdichotomy and global existence of M+, then these two properties persist in a neighborhoodof 0 which agrees either with the whole real line or with an open negative half-line; and inthis last case, the ED fails at the right end value. The properties of ED and of global existenceof M+ are fundamental to guarantee the solvability of classical minimization problems givenby linear–quadratic control processes.
PB Springer
SN 1040-7294
YR 2018
FD 2018
LK http://uvadoc.uva.es/handle/10324/41602
UL http://uvadoc.uva.es/handle/10324/41602
LA spa
NO Journal of Dynamics and Differential Equations 31 (3) (2019), 1397–1426
DS UVaDOC
RD 19-nov-2024