Existence of bounded uniformly continuous mild solutions on \(\mathbb R\) of evolution equations and their asymptotic behaviour

DOI10.1016/j.jmaa.2013.03.034zbMath1304.47051arXiv1108.3398OpenAlexW2962984552MaRDI QIDQ488688

Bolis Basit, Hans F. Günzler

Publication date: 26 January 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.3398

zbMATH Keywords

evolution equationsGreen functionglobal solutionsalmost periodicalmost automorphicnon-resonancebounded uniformly continuous solutions

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Linear differential equations in abstract spaces (34G10)

Related Items

A new existence theory for periodic solutions to evolution equations

Cites Work

• The operator equation \(AX-XB=C\) with unbounded operators \(A\) and \(B\) and related abstract Cauchy problems
• Difference property for perturbations of vector-valued Levitan almost periodic functions and their analogs
• Pseudo almost automorphic solutions to semilinear differential equations in Banach spaces
• Semigroups of linear operators and applications to partial differential equations
• The operator equation \(AX-XB=C\), admissibility, and asymptotic behavior of differential equations
• Asymptotic behavior of solutions of systems of neutral and convolution equations
• Evolution semigroups and sums of commuting operators: A new approach to the admissibility theory of function spaces
• Harmonic analysis and asymptotic behavior of solutions to the abstract Cauchy problem
• Relations between different types of spectra and spectral characterizations
• A short course on operator semigroups
• Generalized vector valued almost periodic and ergodic distributions
• Solutions presque-périodiques des équations hyperboliques
• SPECTRAL PROPERTIES OF THE OPERATOR EQUATION AX + XB = Y
• Almost automorphic solutions of evolution equations
• Almost Automorphic Functions on Groups
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item