Boundedness and almost periodicity of solutions of partial functional differential equations
type: Item
instance of: scholarly article
title: Boundedness and almost periodicity of solutions of partial functional differential equations
zbMATH Open document ID: 1011.34068
author: Toshiki Naito
author: Nguyen Van Minh
author: Tetsuo Furumochi
published in: Journal of Differential Equations
publication date: 2002-09-08T00:00:00Z
review text: Necessary and sufficient conditions are studied for the abstract functional-differential equation \[ x'= Ax(t)+ Fx_t+ f(t) \] to have almost-periodic solutions with the same structure of spectrum as \(f\). Here, it is assumed that \(t\) is a real variable and \(x= x(t)\) takes values in a Banach space \(X\). Moreover, \(A\) is the infinitesimal generator of a strongly continuous semigroup, \(x_t(s)= x(t+ s)\) and \(x_t\in C([-r, 0], X)\), where \(r\) is a positive real number. The operator \(F\) is defined as \(F\varphi= \int^0_{-r} d\eta(s) \varphi(s)\).
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 35R10
zbMATH DE Number: 1797538
zbMATH Keywords: boundedness
zbMATH Keywords: almost periodicity
zbMATH Keywords: solutions partial functional
zbMATH Keywords: differential equations
reviewed by: Józef Banaś
MaRDI profile type: Publication
full work available at URL: jdeq.2001.4052
OpenAlex ID: W1996828529
cites work: Ordinary differential equations. An introduction to nonlinear analysis. Transl. from the German by Gerhard Metzen
cites work: Q5617898
cites work: Almost periodic solutions of first- and second-order Cauchy problems
cites work: Harmonic analysis and asymptotic behavior of solutions to the abstract Cauchy problem
cites work: Asymptotic behavior of solutions of systems of neutral and convolution equations
cites work: Almost periodicity of mild solutions of inhomogeneous periodic Cauchy problems
cites work: Stability and periodic solutions of ordinary and functional differential equations
cites work: Q4892866
cites work: Periodic solutions of abstract differential equations with infinite delay
cites work: Q4258125
cites work: Q4254848
cites work: Q4051167
cites work: Q4272980
cites work: Almost periodic differential equations
cites work: Q3906660
cites work: Almost periodic solutions of integral equations
cites work: Oscillation results for linear autonomous partial delay differential equations
cites work: Q3860165
cites work: On the existence of periodic solutions for linear inhomogeneous and quasilinear functional differential equations
cites work: Geometric theory of semilinear parabolic equations
cites work: Functional differential equations with infinite delay
cites work: Existence of almost periodic solutions of some functional differential equations with infinite delay in a Banach space
cites work: Q4789276
cites work: Q5556050
cites work: Periodic and almost periodic solutions of Volterra integral differential equations with infinite memory
cites work: Q3049314
cites work: A Massera type criterion for linear functional differential equations with advance and delay
cites work: Bounded and periodic solutions of differential equations in Banach space
cites work: The existence of periodic solutions of systems of differential equations
cites work: Stable and unstable manifolds for partial functional differential equations
cites work: Exponential stability, exponential expansiveness, and exponential dichotomy of evolution equations on the half-line
cites work: Evolution semigroups and sums of commuting operators: A new approach to the admissibility theory of function spaces
cites work: Asymptotic behavior of one-parameter semigroups of positive operators
cites work: Evolution semigroups and spectral criteria for almost periodic solutions of periodic evolution equations
cites work: A decomposition theorem for bounded solutions and the existence of periodic solutions to periodic differential equations
cites work: New spectral criteria for almost periodic solutions of evolution equations
cites work: The asymptotic behaviour of semigroups of linear operators
cites work: Semigroups of linear operators and applications to partial differential equations
cites work: On the Spectrum of C 0 -Semigroups
cites work: Q4276447
cites work: Weak almost periodicity of convolutions
cites work: Q4340096
cites work: Almost periodicity and stability for solutions to functional differential equations with infinite delay
cites work: Q3821111
cites work: Asymptotically almost periodic solutions of evolution equations in Banach spaces
cites work: Semi-Fredholm operators and periodic solutions for linear functional-differential equations
cites work: Existence and Stability for Partial Functional Differential Equations
cites work: Almost periodic solutions of Volterra equations
cites work: The operator equation \(AX-XB=C\), admissibility, and asymptotic behavior of differential equations
cites work: Theory and applications of partial functional differential equations
cites work: Stability theory and the existence of periodic solutions and almost periodic solutions
DOI: 10.1006/JDEQ.2001.4052
description: scientific article; zbMATH DE number 1797538