General theorems for stability and boundedness for nonlinear functional discrete systems

Journal of Mathematical Analysis and Applications

Volumn 279, Issue 2, 2003, Pages 639-650

  Raffoul, Youssef N ^a  

^a UNIVERSITY OF DAYTON   (United States)

Author keywords

Lyapunov functionals; Nonlinear discrete systems; Uniform boundedness; Uniform stability

Indexed keywords

EID: 0037845209     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(03)00051-9     Document Type: Article

References (12)

1. R. Agarwal, P.Y. Pang, On a generalized difference system, Nonlinear Anal. 30 (1997) 365-376.
2. T.A. Burton, H. Quichang, W.E. Mahfoud, Liapunov functionals of convolution type, J. Math. Anal. Appl. 106 (1985) 249-272.
3. M.R. Crisci, V.B. Kolmanovskii, A. Vecchio, Boundedness of discrete Volterra equations, J. Math. Anal. Appl. 211 (1997) 106-130.
4. S. Elaydi, Periodicity and stability of linear Volterra difference systems, J. Math. Anal. Appl. 181 (1994) 483-492.
5. S. Elaydi, S. Murakami, Uniform asymptotic stability in linear Volterra difference equations, J. Differ. Equations 3 (1998) 203-218.
6. P. Eloe, M. Islam, Y. Raffoul, Uniform asymptotic stability in nonlinear Volterra discrete systems, Comput. Math. Appl., Special Issue Adv. Differ. Equations IV, to appear.
7. M. Islam, Y. Raffoul, Uniform asymptotic stability in linear Volterra difference equations, Panamer. Math. J., to appear.
8. W. Kelly, A. Peterson, Difference Equations. An Introduction with Applications, Academic Press, 2000.
9. R. Medina, Asymptotic behavior of Volterra difference equations, Comput. Math. Appl., to appear.
10. R. Medina, The asymptotic behavior of the solutions of a Volterra difference equation, Comput. Math. Appl. 181 (1994) 19-26.
11. R. Medina, Solvability of discrete Volterra equations in weighted spaces, Dynam. Systems Appl. 5 (1996) 407-422.
12. Y. Raffoul, Boundedness and periodicity of Volterra systems of difference equations, J. Differ. Equations 4 (1998) 381-393.