Stability and almost periodicity of solutions of ill-posed abstract cauchy problems

Proceedings of the American Mathematical Society

Volumn 125, Issue 1, 1997, Pages 235-241

  Delaubenfels, R ^a   Phóng, Vũ Quoc ^a  

^a OHIO UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33646937969     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-97-03575-2     Document Type: Article

References (18)

1. W. Arendt and C.J.K. Batty, Tauberian theorems and stability of one-parameter semigroups, Trans. Amer. Math. Soc. 306 (1988), 837-852. MR 89g:47053
2. C.J.K. Batty and Vu Quôc Phông, Stability of individual elements under one-parameter semigroups, Trans. Amer. Math. Soc. 322 (1990), 805-818. MR 91c:47072
3. R. deLaubenfels, Existence families, functional calculi and evolution equations. Lecture Notes in Math., vol. 1570, Springer, Berlin, 1994. MR 9Gb:47047
4. R. deLaubenfels and S. Kantorovitz, Laplace and Laplace-Stieltjes spaces, 3. Functional. Anal. 116 (1993), 1-61. MR 94g:47015
5. K. DeLeeuw and I. Glicksberg, Applications of almost periodic compactifications, Acta Mathematica 105 (1961), 63-97. MR 24:A1632
6. O. ElMennaoui, Asymptotic behaviour of integrated semigroups, J. Comp. Appl. Math. 54 (1994), 351-369. MR 96a:47067
7. J. Esterle, E. Strouse and F. Zouakia, Stabilité asymptotique de certains semigroupes dàpérateurs, J. Operator Theory 28 (1992), 203-227. MR 95f:43001
8. J.A. Goldstein, Semigroups of linear operators and applications, Oxford Univ. Press, Oxford, 1985. MR 87c:47056
9. S. Huang, Characterizing spectra of closed operators through existence of slowly growing solutions of their Cauchy problems, Studia Math. 116 (1995), 23-41. CMP 96:02
10. S. Kantorovitz, The Hille-Yosida space of an arbitrary operator, J. Math. Anal, and Appl. 136 (1988), 107-111. MR 90a:47097
11. Y. Katznelson and L. Tzafriri, On power-bounded operators, J. Functional Analysis 68 (1986), 313-328. MR 88e:47006
12. S.G. Krein, G.I. Laptev and G.A. Cvetkova, On Hadamard correctness of the Cauchy problem for the equation of evolution, Soviet Math. Dokl. 11 (1970), 763-766. MR 42:637
13. B.M. Levitan and V.V. Zhikov, Almost periodic functions and differential equations, Cambridge Univ. Press, Cambridge, 1982. MR 84g:34004
14. Yu.I. Lyubich and Vu Quôc Phöng, Asymptotic stability of linear differential equations on Banach spaces, Studia Math. 88 (1988), 37-42. MR 89e:47062
15. R. Nagel, One-parameter semigroups of positive operators. Lecture Notes in Math. 1184, Springer, Berlin, 1986. MR 88i:47022
16. Vu Quôc Phöng and Yu.I. Lyubich, A spectral criterion for almost periodicity of oneparameter semigroups, J. Soviet Math. 48 (1990), 644-647. Originally published in: "Teor. Funktsii, Funktsional. Anal, i Prilozhenia", 47, 36-41 (1987). MR 89a:47067
17. Vu Quôc Phöng, Theorems of Katznelson-Tzafriri type for semigroups of operators, J. Functional Analysis 103 (1992), 74-84. MR 93e:47050
18. Vu Quôc Phöng, On the spectrum, complete trajectories and asymptotic stability of linear semidynamical systems, J. Differential Equations 105 (1993), 30-45. MR 94f:47049