A Massera type theorem for almost automorphic solutions of differential equations

Journal of Mathematical Analysis and Applications

Volumn 299, Issue 2, 2004, Pages 587-599

  Liu, James ^a   N'Guérékata, Gaston ^b   van Minh, Nguyen ^a  

^a JAMES MADISON UNIVERSITY   (United States)

^b MORGAN STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 7244245616     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2004.05.046     Document Type: Article

References (30)

1. W. Arendt C.J.K. Batty M. Hieber F. Neubrander Vector-Valued Laplace Transforms and Cauchy Problems Monogr. Math. vol. 96 2001 Birkhäuser Basel
2. S.N. Chow J.K. Hale Strongly limit-compact maps Funkcial. Ekvac. 17 1974 31-38
3. D. Daners P.K. Medina Abstract Evolution Equations, Periodic Problems and Applications Pitman Res. Notes Math. Ser. vol. 279 1992 Longman New York
4. T. Diagana G. N'Guerekata Nguyen Van Minh, Almost automorphic solutions of evolution equations Proc. Amer. Math. Soc. 132 11 2004 3289-3298
5. A.M. Fink Almost Periodic Differential Equations 1974 Springer-Verlag
6. T. Furumochi T. Naito Nguyen Van Minh Boundedness and almost periodicity of solutions of partial functional differential equations J. Differential Equations 180 2002 125-152
7. J.K. Hale Theory of Functional Differential Equations 1977 Springer-Verlag Berlin
8. D. Henry Geometric Theory of Semilinear Parabolic Equations Lecture Notes in Math. 1981 Springer-Verlag Berlin
9. Y. Hino S. Murakami Almost automorphic solutions of abstract functional differential equations J. Math. Anal. Appl. 286 2003 741-752
10. Y. Hino S. Murakami Nguyen Van Minh Decomposition of variation of constants formular for abstract functional differential equations Funkcial. Ekvac. 45 2002 341-372
11. Y. Hino T. Naito Nguyen Van Minh Jong Son Shin Almost Periodic Solutions of Differential Equations in Banach spaces 2002 Taylor and Francis London
12. Z.S. Hu A.B. Mingarelli On a question in the theory of almost periodic differential equations Proc. Amer. Math. Soc. 127 1999 2665-2670
13. R. Johnson A linear almost periodic equation with an almost automorphic solution Proc. Amer. Math. Soc. 82 1981 199-205
14. B.M. Levitan V.V. Zhikov Almost Periodic Functions and Differential Equations 1978 Moscow Univ. Publ. House English translation by 1982 Cambridge University Press
15. Y. Li Z. Lin Z. Li A Massera type criterion for linear functional differential equations with advanced and delay J. Math. Anal. Appl. 200 1996 715-725
16. Y. Li F. Cong Z. Lin W. Liu Periodic solutions for evolution equations Nonlinear Anal. 36 1999 275-293
17. J. Liu T. Naito Nguyen Van Minh Bounded and periodic solutions of infinite delay evolution equations J. Math. Anal. Appl. 286 2003 705-712
18. J.L. Massera The existence of periodic solutions of systems of differential equations Duke Math. J. 17 1952 457-475
19. S. Murakami T. Naito Nguyen Van Minh Massera theorem for almost periodic solutions of functional differential equations J. Math. Soc. Japan 56 2004 247-268
20. T. Naito Nguyen Van Minh R. Miyazaki J.S. Shin A decomposition theorem for bounded solutions and the existence of periodic solutions of periodic differential equations J. Differential Equations 160 2000 263-282
21. T. Naito Nguyen Van Minh J.S. Shin New spectral criteria for almost periodic solution of evolution equations Studia Math. 145 2001 97-111
22. G.M. N'Guerekata Almost Automorphic and Almost Periodic Functions in Abstract Spaces 2001 Kluwer Academic/Plenum New York
23. G.M. N'Guerekata An extension of the Bohr-Neugebauer theorem Dynam. Syst. Appl. 10 2001 451-454
24. G.M. N'Guerekata Almost automorphic solutions of some differential equations in Banach spaces Internat. J. Math. Math. Sci. 23 2000 361-365
25. G.M. N'Guerekata Almost automorphic functions and applications to abstract evolution equations Contemp. Math. 252 1999 71-76
26. G.M. N'Guerekata Almost automorphy, almost periodicity and stability of motions in Banach spaces Forum Math. 13 2001 581-588
27. G.M. N'Guerekata, On almost automorphic solutions of linear operational-differential equations, Internat. J. Math. Math. Sci., in press
28. G.M. N'Guerekata weak almost periodic mild solutions of some linear abstract differential equations in: Proc. Fourth Internat. Conf. Dynamical Systems and Differential Equations May 24-27, 2002, Wilmington, NC, USA 2003 673-683
29. G.M. N'Guerekata Existence and uniqueness of almost automorphic mild solutions to some semilinear abstract differential equations Semigroup Forum 69 2004 80-86
30. J.S. Shin T. Naito Semi-Fredholm operators and periodic solutions for linear functional differential equations J. Differential Equations 153 1999 407-441