Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/wiley/asymptotically-almost-periodic-solutions-of-inhomogeneous-cauchy-yK53Ku03VI
References (32)
-
P. Milnes (1980)
On Vector‐Valued Weakly Almost Periodic FunctionsJournal of The London Mathematical Society-second Series
-
E. Davies (1980)
One-parameter semigroups -
C. Batty, J. Neerven, F. Räbiger (1998)
Tauberian theorems and stability of solutions of the Cauchy problemTransactions of the American Mathematical Society, 350
-
W. Arendt, C. Batty (1988)
Tauberian theorems and stability of one-parameter semigroupsTransactions of the American Mathematical Society, 306
-
C. Batty, V. Phóng (1990)
Stability of individual elements under one-parameter semigroupsTransactions of the American Mathematical Society, 322
-
B. Basit (1997)
Harmonic analysis and asymptotic behavior of solutions to the abstract cauchy problemSemigroup Forum, 54
-
B. Levitan, V. Zhikov (1983)
Almost Periodic Functions and Differential Equations -
C. Batty, J. Neerven, F. Räbiger (1998)
Local spectra and individual stability of uniformly bounded ₀-semigroupsTransactions of the American Mathematical Society, 350
-
W. Arendt, J. Prüss (1992)
Vector-valued Tauberian theorems and asymptotic behavior of linear Volterra equations,Siam Journal on Mathematical Analysis, 23
-
J. Prüss (1993)
Evolutionary Integral Equations And Applications -
(1996)
The asymptotic beha iour of semigroups of linear operators (Birkhau$ ser -
W. Arendt, A. Grabosch, G. Greiner, Ulrich Moustakas, R. Nagel, U. Schlotterbeck, U. Groh, H. Lotz, F. Neubrander (1986)
One-parameter Semigroups of Positive Operators -
J. Korevaar (1982)
On newman’s quick way to the prime number theoremThe Mathematical Intelligencer, 4
-
W. Ruess, V. Phóng (1995)
Asymptotically Almost Periodic Solutions of Evolution Equations in Banach SpacesJournal of Differential Equations, 122
-
Yu. Lyubich, P. Vu (1988)
Asymptotic stability of linear differential equations in Banach spacesStudia Mathematica, 88
-
W. Ruess, W. Summers (1990)
WEAKLY ALMOST PERIODIC SEMIGROUPS OF OPERATORSPacific Journal of Mathematics, 143
-
V. Fong, Yu. Lyubich (1990)
A spectral criterion for the almost periodicity of one-parameter semigroupsJournal of Soviet Mathematics, 48
-
M. Kadets (1969)
On the integration of almost periodic functions with values in a Banach spaceFunctional Analysis and Its Applications, 3
-
M. Ulm (1996)
Asymptotics of a new population model with quiescence, 1996
-
Richard Miller (1964)
On almost periodic differential equationsBulletin of the American Mathematical Society, 70
-
W. Ruess, W. Summers (1989)
Integration of asymptotically almost periodic functions and weak asymptotic almost periodicity -
(1997)
Asymptotics of models for cell populations -
B. Basit (1995)
Some problems concerning different types of vector valued almost periodic functions -
J. Goehring (1986)
THE ENGLISH TRANSLATION -
W. Arendt, C. Batty (1996)
Almost Periodic Solutions of First- and Second-Order Cauchy ProblemsJournal of Differential Equations, 137
-
R. Delaubenfels, V. Phóng (1997)
Stability and almost periodicity of solutions of ill-posed abstract Cauchy problems, 125
-
C. Batty, Z. Brzeźniak, D. Greenfield (1996)
A quantitative asymptotic theorem for contraction semigroups with countable unitary spectrumStudia Mathematica
-
S. Goldberg, Paul Irwin (1979)
Weakly almost periodic vector-valued functions -
A. Ingham (1935)
On Wiener's Method in Tauberian TheoremsProceedings of The London Mathematical Society
-
W. Ruess, W. Summers (1992)
Ergodic theorems for semigroups of operators, 114
-
W. Eberlein (1949)
Abstract ergodic theorems and weak almost periodic functionsTransactions of the American Mathematical Society, 67
-
C. Batty (1996)
Spectral Conditions for Stability of One-Parameter SemigroupsJournal of Differential Equations, 127
- Publisher
- Wiley
- Copyright
- © London Mathematical Society
- ISSN
- 0024-6093
- eISSN
- 1469-2120
- DOI
- 10.1112/S0024609398005657
- Publisher site
- See Article on Publisher Site
Abstract
Let u be a bounded, uniformly continuous, mild solution of an inhomogeneous Cauchy problem on R+: u′(t)+Au(t)+φ(t)(t⩾0). Suppose that u has uniformly convergent means, σ(A)∩iR is countable, and φ is asymptotically almost periodic. Then u is asymptotically almost periodic. Related results have been obtained by Ruess and Vũ, and by Basit, using different methods. A direct proof is given of a Tauberian theorem of Batty, van Neerven and Räbiger, and applications to Volterra equations are discussed. 1991 Mathematics Subject Classification 34C28, 44A10, 47D03.
Journal
Bulletin of the London Mathematical Society – Wiley
Published: May 1, 1999