On the boundedness of the solutions in nonlinear discrete Volterra difference equations

Advances in Difference Equations

Volumn 2012, Issue , 2012, Pages

  Györi, István ^a   Awwad, Essam ^a,b  

^a UNIVERSITY OF PANNONIA   (Hungary)

^b BENHA UNIVERSITY   (Egypt)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84870066872     PISSN: 16871839     EISSN: 16871847     Source Type: Journal    
DOI: 10.1186/1687-1847-2012-2     Document Type: Article

References (18)

1. Agarwal, RP: Difference Equations and Inequalities, Theory, Methods, and Application. Marcel Dekker, New York, 2 (2000)
2. Appleby, JAD, Gyori, I, Reynolds, D: On exact convergence rates for solutions of linear systems of Volterra difference equations. J Diff Equ Appl. 12(12):1257-1275 (2006). doi:10.1080/10236190600986594
3. Choi, SK, Koo Nam, Jip: Asymptotic property of linear Volterra difference systems. J Math Anal Appl. 321, 260-272 (2006). doi:10.1016/j.jmaa.2005.08.028
4. Cuevas, C, Pinto, M: Asymptotic behavior in Volterra difference systems with unbounded delay. J Comput Appl Math. 113, 217-225 (2000). doi:10.1016/S0377-0427(99)00257-5
5. Elaydi, S: An Introduction to Difference Equations. Springer-Verlag, New York, 3 (2005)
6. Elaydi, S, Murakami, S, Kamiyama, E: Asymptotic equivalence for difference equations with infinite delay. J Diff Equ Appl. 5, 1-23 (1999). doi:10.1080/10236199908808167
7. Furumochi, T, Murakami, S, Nagabuchi, Y: A generalization of Wiener's lemma and its application to Volterra difference equations on a Banach space. J Diff Eq Appl. 10(13-15):1201-1214 (2004). doi:10.1080/10236190410001652748
8. Györi, I, Horváth, L: Asymptotic representation of the solutions of linear Volterra difference equations. Adv Diff Equ 22 (2008). (Art. ID 932831), (2008)
9. Györi, I, Reynolds, DW: On admissimility of the resolvent of discrete Volterra equations. J Diff Equ Appl. 16(12):1393-1412 (2010). doi:10.1080/10236190902824196
10. Györi, I, Reynolds, DW: Sharp conditions for boundedness in linear discrete Volterra equations. J Diff Equ Appl. 15, 1151-1164 (2009). doi:10.1080/10236190902932726
11. Kolmanovskii, VB, Castellanos-Velasco, E, Torres-Muñoz, JA: A survey: stability and boundedness of Volterra difference equations. Nonlinear Anal. 53, 861-928 (2003). doi:10.1016/S0362-546X(03)00021-X
12. Kolmanovskii, V, Shaikhet, L: Some conditions for boundedness of solutions of difference Volterra equations. Appl Math Lett. 16, 857-862 (2003). doi:10.1016/S0893-9659(03)90008-5
13. Medina, M: Asymptotic properties of solutions of nonlinear difference equations. J Comput Appl Math. 70, 57-66 (1996). doi:10.1016/0377-0427(95)00139- 5
14. Medina, R, Pinto, M: Asymptotic equivalence and asymptotic behavior of difference systems. Commun Appl Anal. 1, 511-523 (1997)
15. Pachpatte, BG: Qualitative properties of solutions of certain Volterra type difference equations. Tamsui Oxf J Math Sci. 26(3):273-285 (2010)
16. Yihong, Song, Baker, CTH: Admissibility for discrete Volterra equations. J Diff Equ Appl. 12(5):433-457 (2006). doi:10.1080/10236190600563260
17. Yihong, Song, Baker, CTH: Linearized stability analysis of discrete Volterra equations. J Math Anal Appl. 294, 310-333 (2004). doi:10.1016/j.jmaa. 2004.02.019
18. Lipovan, O: On the asymptotic behavior of solutions to some nonlinear integral equations of convolution type. Dyn Contin Discrete Impuls Syst. 16, 147-154 (2009)