Stability in delay Volterra difference equations of neutral type
DOI:
https://doi.org/10.4067/S0716-09172015000300003Keywords:
Banach’s Fixed point theorem, Volterra difference equation, Asymptotic stability.Abstract
Sufficient conditions for the zero solution of a certain class of neutral Volterra difference equations with variable delays to be asymptotically stable are obtained. The Banach’s fixed point theorem is employed in proving our results.References
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[2] A. Ardjouni, and A. Djoudi; Stability in linear neutral difference equations with variable delays, Mathematica Bohemica, No. 3, pp. 245-258, (2013).
[3] S. Elaydi, Periodicity and stability of linear Volterra difference systems, Journal of Mathematical Analysis and Applications, 181, pp. 483-492, (1994).
[4] S. Elaydi, An Introduction to Difference Equations, Springer, New York, (1999).
[5] M. Islam and E. Yankson, Boundedness and stability in nonlinear delay difference equations employing fixed point theory, Electronic Journal of Qualitative Theory of Differential Equations, No. 26, pp. 1-18, (2005).
[6] W. G. Kelly and A. C. Peterson, Difference Equations : An Introduction with Applications, Academic Press, (2001).
[7] Y. N. Raffoul, Stability and periodicity in discrete delay equations, Journal of Mathematical Analysis and Applications, 324, No. 2, pp. 1356-1362, (2006).
[8] Y. N. Raffoul, Periodicity in general delay nonlinear difference equations using fixed point theory, Journal of Difference Equations and Applications, 10, No. 1315, pp. 1229-1242, (2004).
[9] Y. N. Raffoul, General theorems for stability and boundedness for nonlinear functional discrete systems, Journal of Mathematical Analysis and Applications, 279, pp. 639-650, (2003).
[10] D. R. Smart, Fixed point theorems ; Cambridge Tracts in Mathematics, No. 66. Cambridge University Press, London-New York, (1974).
[11] E. Yankson, Stability in discrete equations with variable delays, Electronic Journal of Qualitative Theory of Differential Equations, No. 8, pp. 1-7, (2009).
[12] E. Yankson, Stability of Volterra difference delay equations, Electronic Journal of Qualitative Theory of Differential Equations, No. 20, pp. 1-14, (2006).
Published
2015-09-01
How to Cite
[1]
E. Yankson and E. K. Essel, “Stability in delay Volterra difference equations of neutral type”, Proyecciones (Antofagasta, On line), vol. 34, no. 3, pp. 229-241, Sep. 2015.
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