- Volume 55 Issue 6
DOI QR Code
STABILITY IN FUNCTIONAL DIFFERENCE EQUATIONS WITH APPLICATIONS TO INFINITE DELAY VOLTERRA DIFFERENCE EQUATIONS
- Raffoul, Youssef N. (Department of Mathematics University of Dayton)
- Received : 2018.01.17
- Accepted : 2018.08.03
- Published : 2018.11.30
We consider a functional difference equation and use fixed point theory to obtain necessary and sufficient conditions for the asymptotic stability of its zero solution. At the end of the paper we apply our results to nonlinear Volterra infinite delay difference equations.
- J. Cermak, Difference equations in the qualitative theory of delay differential equations, in Proceedings of the Sixth International Conference on Difference Equations, 391-398, CRC, Boca Raton, FL, 2004.
- S. N. Elaydi, An Introduction to Difference Equations, second edition, Undergraduate Texts in Mathematics, Springer-Verlag, New York, 1999.
- W. Kelley and A. Peterson, Difference Equations an Introduction with Applications, Academic Press, 2001.
- J. Migda, Asymptotic behavior of solutions of nonlinear difference equations, Math. Bohem. 129 (2004), no. 4, 349-359.
- C. Qian and Y. Sun, On global attractivity of nonlinear delay difference equations with a forcing term, J. Difference Equ. Appl. 11 (2005), no. 3, 227-243. https://doi.org/10.1080/10236190500035252
- Y. N. Raffoul and E. Yankson, Existence of bounded solutions for Almost-Linear Volterra difference equations using fixed point theory and Lyapunov, Functionals Nonlinear Studies 21 (2014), 663-674.
- C. Tunc, New stability and boundedness results to Volterra integro-differential equations with delay, J. Egyptian Math. Soc. 24 (2016), no. 2, 210-213. https://doi.org/10.1016/j.joems.2015.08.001
- C. Tunc, A note on the qualitative behaviors of non-linear Volterra integro-differential equation, J. Egyptian Math. Soc. 24 (2016), no. 2, 187-192. https://doi.org/10.1016/j.joems.2014.12.010
- D. Zhang and B. Shi, Global behavior of solutions of a nonlinear difference equation, Appl. Math. Comput. 159 (2004), no. 1, 29-35. https://doi.org/10.1016/j.amc.2003.08.125
- H. Zhu and L. Huang, Asymptotic behavior of solutions for a class of delay difference equation, Ann. Differential Equations 21 (2005), no. 1, 99-105.