2006/12/07 by Qing Liu, Nguyen Van Minh, Nguyễn Văn Minh +7
Computer Science · Engineering · Mathematics · #34C27 #47D06 #Advanced Mathematical Modeling in Engineering #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations #math.DS #math.FA #msc:34C27 #msc:47D06
paper · pdf · doi:10.48550/arxiv.math/0612197
18 pages
openalex publication_date 2006/12/07 · arxiv created 2007/09/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper is concerned with conditions for the existence of almost periodic solutions of the following abstract functional differential equation u(t) = Au(t) + [\cal Bu](t) +f(t), where A is a closed operator in a Banach space \X, \cal B is a general bounded linear operator in the function space of all \X-valued bounded and uniformly continuous functions that satisfies a so-called \it autonomous condition. We develop a general procedure to carry out the decomposition that does not need the well-posedness of the equations. The obtained conditions are of Massera type, which are stated in terms of spectral conditions of the operator \cal A+\cal B and the spectrum of f. Moreover, we give conditions for the equation not to have quasi-periodic solutions with different structures of spectrum. The obtained results extend previous ones.