Stepanov-like pseudo-almost periodic mild solutions to perturbed nonautonomous evolution equations with infinite delay

Nonlinear Analysis, Theory, Methods and Applications

Volumn 71, Issue 11, 2009, Pages 5381-5391

  Hu, Zhanrong ^a   Jin, Zhen ^a  

^a NORTH UNIVERSITY OF CHINA   (China)

Author keywords

Exponential dichotomy; Infinite delay; Perturbed nonautonomous evolution equations; Pseudo almost periodic; Stepanov like pseudo almost periodic

Indexed keywords

EXPONENTIAL DICHOTOMY; INFINITE DELAY; PERTURBED NONAUTONOMOUS EVOLUTION EQUATIONS; PSEUDO-ALMOST PERIODIC; STEPANOV-LIKE PSEUDO-ALMOST PERIODIC;

DIFFERENTIAL EQUATIONS; FOURIER SERIES;

MATHEMATICAL OPERATORS;

EID: 68349121598     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2009.04.032     Document Type: Article

References (38)

1. Diagana T. Stepanov-like pseudo almost periodicity and its applications to some nonautonomous differential equations. Nonlinear Anal. TMA 69 (2008) 4277-4285
2. Diagana T. Stepanov-like pseudo almost periodic functions and there applications to differential equations. Comm. Math. Anal. 3 1 (2007) 9-18
3. Acquistapace P., and Terreni B. A unified approach to abstract linear parabolic equations. Rend. Sem. Mat. Univ. Padova 78 (1987) 47-107
4. Maniar L., and Schnaubelt R. Almost periodicity of inhomogeneous parabolic evolution equations. Lecture Notes in Pure and Appl. Math. vol. 234 (2003), Dekker, New York 299-318
5. Ding H.S., Liang J., N'Guérékata G.M., and Xiao T.J. Pseudo almost periodicity to some nonautonomous evolution equations with delay. Nonlinear Anal. TMA 67 (2007) 1412-1418
6. Ding H.S., Liang J., N'Guérékata G.M., and Xiao T.J. Mild pseudo almost periodic solutions of nonautonomous semilinear evolution equations. Math. Comput. Modelling 45 (2007) 579-584
7. Xiao T.J., Zhu X.X., and Liang J. Pseudo almost automorphic mild solutions to nonautonomous differential equations and applications. Nonlinear Anal. TMA 70 (2009) 4079-4085
8. Acquistapace P. Evolution operators and strong solution of abstract linear parabolic equations. Differential Integral Equations 1 (1988) 433-457
9. Yagi A., and Terreni B. Parabolic equations in which the coefficients are generators of infinitely differentiable semigroups II. Funkcial. Ekvac. 33 (1990) 139-150
10. Yagi A. Abstract quasilinear evolution equations of parabolic type in Banach spaces. Boll. Un. Mat. Ital. B 5 7 (1991) 341-368
11. Engel K.J., and Nagel R. One Parameter Semigroups for Linear Evolution Equations. Graduate Texts in Mathematics (2000), Springer-Verlag
12. Coppel W.A. Dichotomies in Stability Theory (1978), Springer-Verlag
13. Henry D. Geometric Theory of Semilinear Parabolic Equations (1981), Springer-Verlag
14. Chicone C., and Latushkin Y. Evolution semigroups in dynamical systems and differential equations. Proc. Amer. Math. Soc. (1999)
15. Burton T.A., and Zhang B. Periodic solutions of abstract differential equations with infinite delay. J. Differential Equations 90 (1991) 357-396
16. Diagana T. Pseudo almost periodic solutions to some differential equations with infinite delay. Electron. J. Differential Equations 2006 79 (2006) 1-10
17. Diagana T., and N'Guérékata G.M. Pseudo almost periodic mild solutions to hyperbolic evolution equations in abstract intermediate Banach spaces. Appl. Anal. 85 6 (2006) 769-780
18. Diagana T., Mahop C.M., N'Guérékata G.M., and Toni B. Existence and uniqueness of pseudo almost periodic solutions to some classes of semilinear differential equations and applications. Nonlinear Anal. TMA 64 (2006) 2442-2453
19. Li H.X., Huang F.L., and Li J.Y. Composition of pseudo almost-periodic functions and semilinear differential equations. J. Math. Anal. Appl. 255 (2001) 436-446
20. Cuevas C., and Pinto M. Existence and uniqueness of pseudo almost periodic solutions of semilinear Cauchy problems with non dense domain. Nonlinear Anal. TMA 45 (2001) 73-83
21. Amir B., and Maniar L. Composition of pseudo-almost periodic functions and Cauchy problems with operator of nondense domain. Ann. Math. Blaise Pascal 6 (1999) 1-11
22. Ait Dads E., Ezzinbi K., and Arino O. Pseudo almost periodic solution for some differential equation in a Banach space. Nonlinear Anal. TMA 28 (1997) 1141-1155
23. Diagana T. Pseudo almost periodic solutions to some differential equations. Nonlinear Anal. TMA 60 (2005) 1277-1286
24. N'Guérékata G.M., and Pankov A. Stepanov-like almost automorphic functions and monotone evolution equations. Nonlinear Anal. TMA 68 (2008) 2658-2667
25. Lee H., and Alkahby H. Stepanov-like almost automorphic solutions of nonautonomous semilinear evolution equations with delay. Nonlinear Anal. 69 (2008) 2158-2166
26. Zhang C.Y. Pseudo almost periodic solutions of some differential equations. J. Math. Anal. Appl. 151 (1994) 62-76
27. Zhang C.Y. Pseudo almost periodic solutions of some differential equations II. J. Math. Anal. Appl. 192 (1995) 543-561
28. Zhang C.Y. Integration of vector-valued pseudo almost periodic functions. Proc. Amer. Math. Soc. 121 (1994) 167-174
29. C.Y. Zhang, Pseudo almost periodic functions and their applications, Thesis, The University of Western Ontario, 1992
30. Ait Dads E., and Ezzinbi K. Pseudo almost periodic solutions of some delay differential equations. Math. Anal. Appl. 201 (1996) 840-850
31. Diagana T., and Hernández E.M. Existence and uniqueness of pseudo almost periodic solutions to some abstract partial neutral functional differential equations and applications. J. Math. Anal. Appl. 327 (2007) 776-791
32. Hernández E.M., and Henriquez H. Pseudo almost periodic solutions for non-autonomous neutral differential equations with unbounded delay. Nonlinear Anal. RWA 9 (2008) 430-437
33. Diagana T. Existence and uniqueness of pseudo almost periodic solutions to some classes of partial evolution equations. Nonlinear Anal. TMA 66 (2007) 384-395
34. Fatajou S., Van Minh N., N'Guérékata G.M., and Pankov A. Stepanov-like almost automorphic solutions for some nonautonomous evolution equations. Electron. J. Differential Equations 2007 121 (2007) 1-11
35. Diagana T., and N'Guérékata G. Stepanov-like almost automorphic functions and applications to some semilinear equations. Appl. Anal. 86 6 (2007) 723-733
36. N'Guérékata G.M. Almost Automorphic Functions and Almost Periodic Functions in Abstract Spaces (2001), Kluwer Academic, Plenum, New York, London, Moscow
37. Pankov A. Bounded and Almost Periodic Solutions of Nonlinear Operator Differential Equations (1990), Kluwer, Dordrecht
38. Fink A.M. Almost Periodic Differential Equations. Lecture Notes in Mathematics vol. 377 (1974), Springer-Verlag, New York, Berlin