AP_r solutions for linear functional difference equations with infinite delay with/without Favard's property

References

• T.A. Burton, Stability and Periodic Solutions of Ordinary and Functional Differential Equations, Academic Press, London, 1985.
   Google Scholar
• T. Caraballo and D. Cheban, Almost periodic and almost automorphic solutions of linear differential/difference equations without Favard's separation condition. I, J. Differ. Equ. 246 (2009), pp. 108–128. doi: 10.1016/j.jde.2008.04.001
   Web of Science ®Google Scholar
• T. Caraballo and D. Cheban, Almost periodic and almost automorphic solutions of linear differential/difference equations without Favard's separation condition. II, J. Differ. Equ. 246 (2009), pp. 1164–1186. doi: 10.1016/j.jde.2008.07.025
   Web of Science ®Google Scholar
• S.N. Chow and J.K. Hale, Strongly limit-compact maps, Funkcial. Ekvac. 17 (1974), pp. 31–38.
   Google Scholar
• C. Corduneanu, Almost periodic discrete processes, Libertas Math. 2 (1982), pp. 159–169.
   Google Scholar
• C. Corduneanu, Almost Periodic Oscillations and Waves, Springer, New-York, 2009.
   Google Scholar
• C. Corduneanu, Y. Li, and M. Mahdavi, Functional Differential Equations, Wiley, Hoboken, NJ, 2016.
   Google Scholar
• T. Diagana, Pseudo Almost Periodic Functions in Banach Spaces, Nova Science Publ, Inc., New-York, 2007.
   Google Scholar
• T. Diagana, Almost periodic solutions for some higher-order nonautonomous differential equations with operator coefficients, Math. Comput. Model. 54 (2011), pp. 2672–2685. doi: 10.1016/j.mcm.2011.06.050
   Google Scholar
• T. Diagana, Almost periodic solutions to some second-order nonautonomous differential equations, Proc. Am. Math. Soc. 140 (2012), pp. 279–289. doi: 10.1090/S0002-9939-2011-10970-5
   Web of Science ®Google Scholar
• S. Elaydi, An Introduction to Difference Equations, 3rd ed., Springer, New-York, 2005.
   Google Scholar
• S. Elaydi, S. Murakami, and E. Kamiyama, Asymptotic equivalence for difference equations with infinite delay, J. Differ. Equ. Appl. 5 (1999), pp. 1–23. doi: 10.1080/10236199908808167
   Web of Science ®Google Scholar
• J. Favard, Lecons Les Functions Presque-Periodiques, Gauthier-Villars, Paris, 1933.
   Google Scholar
• A.M. Fink, Almost Periodic Differential Equations, Lecture Notes in Mathematics 377, Springer-Verlag, Berlin, 1974.
   Google Scholar
• Y. Hamaya, Existence of an almost periodic solution in a difference equation with infinite delay, J. Differ. Equ. Appl. 9 (2003), pp. 227–237. doi: 10.1080/1023619021000035836
   Web of Science ®Google Scholar
• Y. Hamaya, Existence of APr almost periodic solutions in linear abstract functional difference/differential equations withs infinite delay, submitting.
   Google Scholar
• Y. Hino and S. Murakami, Favard's property for linear retarded equations with infinite delay, Funkcial. Ekvac. 29 (1986), pp. 11–17.
   Google Scholar
• Y. Hino, S. Murakami, and T. Naito, Functional Differential Equations with Infinite Delay, Lecture Notes in Math. 1473, Springer, Berlin, 1991.
   Google Scholar
• Y. Hino, T. Naito, N.V. Minh, and J.S. Shin, Almost Periodic Solutions of Differential Equations in Banach Spaces, Taylor and Francis, London, 2002.
   Google Scholar
• J. Kato, Favard's separation theorem in functional differential equations, Funkcial. Ekvac. 18 (1975), pp. 85–92.
   Google Scholar
• R. Ortega and M. Tarallo, Almost periodic linear differential equations with non-separated solutions, J. Funct. Anal. 237 (2006), pp. 402–426. doi: 10.1016/j.jfa.2006.03.027
   Web of Science ®Google Scholar
• Y. Raffoul, Qualitative Theory of Volterra Difference Equations, Springer, Cham, 2018.
   Google Scholar
• R.J. Sacker and G.R. Sell, Lifting Properties in Skew-Product Flows with Applications to Differential Equations, AMS Mem. Vol. 11, No. 190, American Mathematical Society, Providence, RI, 1977.
   Google Scholar
• K. Sawano, Exponential asymptotic stability for functional differential equations with infinite retardation, Tohoku Math. J. 31 (1979), pp. 363–382. doi: 10.2748/tmj/1178229804
   Google Scholar
• K. Saito and Y. Hamaya, Global attractivity for Volterra difference equations of convolution type, submitting
   Google Scholar
• C. Wang and R.P. Agarwal, Almost periodic solution for a new type of neutral impulsive stochastic Lasota-Wazewska timescale model, Appl. Math. Lett. 70 (2017), pp. 58–65. doi: 10.1016/j.aml.2017.03.009
   Web of Science ®Google Scholar
• C. Wang, R.P. Agarwal, and D. O'Regan, n0-order Δ-almost periodic functions and dynamic equations, Appl. Anal. 97 (2018), pp. 2626–2654. doi: 10.1080/00036811.2017.1382689
   Web of Science ®Google Scholar
• J. Wu, Z. Li, and Z. Wang, Remarks on “periodic solutions of linear Volterra equations”, Funkcial. Ekvac. 30 (1987), pp. 105–109.
   Google Scholar
• T. Yoshizawa, Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions, Applied Mathematical Sciences 14, Springer-Verlag, Berlin, 1975.
   Google Scholar