Almost automorphic solutions to integral equations on the line

Semigroup Forum

Volumn 79, Issue 3, 2009, Pages 461-472

  Cuevas, Claudio ^a   Lizama, Carlos ^b  

^a FEDERAL UNIVERSITY OF PERNAMBUCO   (Brazil)

^b UNIVERSIDAD DE SANTIAGO DE CHILE   (Chile)

Author keywords

Almost automorphic function; Integral resolvent family; Semilinear integro differential equations

Indexed keywords

EID: 76349114928     PISSN: 00371912     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00233-009-9154-0     Document Type: Article

References (24)

1. Araya, D., Lizama, C.: Almost automorphic mild solutions to fractional differential equations. Nonlinear Anal. Ser. A: Theory Methods Appl. 69(11), 3692-3705 (2008).
2. Arendt, W., Batty, C., Hieber, M., Neubrander, F.: Vector-Valued Laplace Transforms and Cauchy Problems. Monographs in Mathematics, vol. 96. Birkhäuser, Basel (2001).
3. Basit, B.: Harmonic analysis and asymptotic behavior of solutions to the abstract Cauchy problem. Semigroup Forum 54, 58-74 (1997).
4. 0-semigroups and solutions of linear and semilinear abstract differential equations. Russ. J. Math. Phys. 13(1), 13-30 (2006).
5. Bazhlekova, E.: Fractional evolution equations in Banach spaces. Ph. D. Thesis, Eindhoven University of Technology (2001).
6. Bugajewski, D., Diagana, T.: Almost automorphy of the convolution operator and applications to differential and functional differential equations. Nonlinear Stud. 13(2), 129-140 (2006).
7. Clément, Ph., Da Prato, G.: Existence and regularity results for an integral equation with infinite delay in a Banach space. Integr. Equ. Oper. Theory 11, 480-500 (1988).
8. Diagana, T.: Some remarks on some second-order hyperbolic differential equations. Semigroup Forum 68, 357-364 (2004).
9. Diagana, T., N'Guérékata, G. M.: Almost automorphic solutions to semilinear evolution equations. Funct. Differ. Equ. 13(2), 195-206 (2006).
10. Goldstein, J. A., N'Guérékata, G. M.: Almost automorphic solutions of semilinear evolution equations. Proc. Am. Math. Soc. 133(8), 2401-2408 (2005).
11. Gorenflo, R., Mainardi, F.: On Mittag-Leffler-type functions in fractional evolution processes. J. Comput. Appl. Math. 118, 283-299 (2000).
12. Gripenberg, G., Londen, S.-O., Staffans, O.: Volterra Integral and Functional Equations. Encyclopedia of Mathematics and Applications, vol. 34. Cambridge University Press, Cambridge (1990).
13. Liang, J., Zhang, J., Xiao, T. J.: Composition of pseudo almost automorphic and asymptotically almost automorphic functions. J. Math. Anal. Appl. 340(2), 1493-1499 (2008).
14. Liu, J., N'Guérékata, G. M., van Minh, N.: Almost automorphic solutions of second order evolution equations. Appl. Anal. 84(11), 1173-1184 (2005).
15. Lizama, C.: Regularized solutions for abstract Volterra equations. J. Math. Anal. Appl. 243, 278-292 (2000).
16. Lizama, C.: On approximation and representation of k-regularized resolvent families. Integr. Equ. Oper. Theory 41(2), 223-229 (2001).
17. Lizama, C., Sánchez, J.: On perturbation of k-regularized resolvent families. Taiwan. J. Math. 7(2), 217-227 (2003).
18. Lizama, C., Poblete, V.: On multiplicative perturbation of integral resolvent families. J. Math. Anal. Appl. 327(2), 1335-1359 (2007).
19. N'Guerekata, G. M.: Almost Automorphic and Almost Periodic Functions in Abstract Spaces. Kluwer Acad/Plenum, New York-Boston-Moscow-London (2001).
20. N'Guérékata, G. M.: Existence and uniqueness of almost automorphic mild solutions of some semilinear abstract differential equations. Semigroup Forum 69, 80-86 (2004).
21. N'Guérékata, G. M.: Topics in Almost Automorphy. Springer, New York (2005).
22. Nunziato, J. W.: On heat conduction in materials with memory. Q. Appl. Math. 29, 187-204 (1971).
23. Prüss, J.: Evolutionary Integral Equations and Applications. Monographs Math., vol. 87. Birkhäuser, Basel (1993).
24. Shaw, S. Y., Chen, J. C.: Asymptotic behavior of (a, k)-regularized families at zero. Taiwan. J. Math. 10(2), 531-542 (2006).