Pseudo almost periodic mild solutions to hyperbolic evolution equations in intermediate Banach spaces

International Journal of Phytoremediation

Volumn 85, Issue 6-7, 2006, Pages 769-780

  Diagana, Toka ^a   N'gué ré kata, Gaston M ^b  

^a HOWARD UNIVERSITY   (United States)

^b MORGAN STATE UNIVERSITY   (United States)

Author keywords

2000 Mathematics Subject Classifications:34G20; 47A55; Almost periodic; Analytic semigroup; Hyperbolic evolution equation; Hyperbolic semigroup; Pseudo almost periodic; Sectorial operator

Indexed keywords

EID: 85016845302     PISSN: 15226514     EISSN: 15497879     Source Type: Journal    
DOI: 10.1080/00036810600708499     Document Type: Article

References (25)

1. Amir, B, and Maniar, L. 1999. Composition of pseudo-almost periodic functions and Cauchy problems with operator of nondense domain. Annales Mathematiques Blaise Pascal, 6 (1): 1-11.
2. Boulite, S, Maniar, L, and N'Guérekata, GM. 2005. Almost periodic solutions for hyperbolic semilinear evolution equations. Semigroup Forum, 71: 231-240.
3. Corduneanu, C. 1989. Almost Periodic Functions, 2nd, New York: Chelsea.
4. Cuevas, C, and Pinto, M. 2001. Existence and uniqueness of pseudo almost periodic solutions of semilinear Cauchy problems with non dense domain. Nonlinear Analysis, Series A: Theory Methods, 45 (1): 73-83.
5. Diagana, T. 2005. Pseudo almost periodic solutions to some differential equations. Nonlinear Analysis, 60 (7): 1277-1286.
6. Diagana, T. 2005. Existence and uniqueness of pseudo almost periodic solutions to some classes of partial evolution equations. Nonlinear Analysis (TMA), (In press)
7. Diagana, T, Mahop, CM, and N'Guérékata, GM. 2006. Pseudo almost periodic solutions to some semilinear differential equations. Mathematical and Computer Modelling, 43(1-2): 89-96.
8. Diagana, T, Mahop, CM, N'Guérékata, GM, and Toni, B. 2006. Existence and uniqueness of pseudo almost periodic solutions to some classes of semilinear differential equations and applications. Nonlinear Analysis, 64 (11): 2442-2453.
9. Engel, KJ, and Nagel, R. 1999. “ One Parameter Semigroups for Linear Evolution Equations ”. In Graduate texts in Mathematics 194, Berlin: Springer-Verlag.
10. Fink, AM. 1974. “ Almost Periodic Differential Equations ”. In Lecture Notes in Mathematics, Vol. 377, New York-Berlin: Springer-Verlag.
11. Goldstein, JA, and N'Guérékata, GM. Almost automorphic solutions of semilinear evolution equations. Proceedings of the American Mathematical Society. Vol. 133(8), pp. 2401-2408.
12. Hernández, EM, and Pelicer, ML. 2005. Asymptotically almost periodic and almost periodic solutions for partial neutral differential equations. Applied Mathematics Letters, 18 (11): 1265-1272.
13. Henríquez, HR, and Vásquez, CH. 1999. Almost periodic solutions of abstract retarded functional-differential equations with unbounded delay. Acta Applicandae Mathematicae, 57 (2): 105-132.
14. Hino, Y, and Murakami, S. 2002. Limiting equations and some stability properties for asymptotically almost periodic functional differential equations with infinite delay. Tôhoku Mathematical Journal, 54 (2): 239-257.
15. Hino, Y, Murakami, S, and Naito, T. 1991. “ Functional-Differential Equations with Infinite Delay ”. In Lecture Notes in Mathematics, Vol. 1473, Berlin: Springer-Verlag.
16. Li, H-X, Huang, F-L, and Li, J-Y. 2001. Composition of pseudo almost-periodic functions and semilinear differential equations. Journal of Mathematical Analysis and Applications, 255 (2): 436-446.
17. Lunardi, A. 1995. Analytic Semigroups and Optimal Regularity in Parabolic Problems, Basel: Birkhäuser.
18. Minh Man, N, and Van Minh, N. 2004. On the existence of quasi periodic and almost periodic solutions of neutral functional differential equations. Communications on Pure and Applied Analysis, 3 (2): 291-300.
19. N'Guérékata, GM. 2001. Almost Automorphic Functions and Almost Periodic Functions in Abstract Spaces, New York-London-Moscow: Kluwer Academic/Plenum Publishers.
20. N'Guérékata, GM. 2004. Existence and uniqueness of almost automorphic mild solution to some semilinear abstract differential equations. Semigroup Forum, 69: 80-86.
21. N'Guérékata, GM. 2005. Topics Almost Automorphy, New York, Boston, Dordrecht, London, Moscow: Springer.
22. Yuan, R. 1998. Existence of almost periodic solutions of neutral functional-differential equations via Liapunov-Razumikhin function. Zeitschrift fur Angewandte Mathematik und Physik, 49 (1): 113-136.
23. Zhang, CY. 1994. Pseudo almost periodic solutions of some differential equations. Journal of Mathematical Analysis and Applications, 151: 62-76.
24. Zhang, CY. 1995. Pseudo almost periodic solutions of some differential equations II. Journal of Mathematical Analysis and Applications, 192: 543-561.
25. Zhang, CY. 1994. Integration of vector-valued pseudo almost periodic functions. Proceedings of the American Mathematical Society. 1994. Vol. 121, pp. 167-174.