Discrete Halanay-type inequalities and applications

Nonlinear Analysis, Theory, Methods and Applications

Volumn 55, Issue 6, 2003, Pages 669-678

  Liz, Eduardo ^a   Ivanov, Anatoli ^b   Ferreiro, Juan Bosco ^c  

^a UNIVERSITY OF VIGO   (Spain)

^b PENNSYLVANIA STATE UNIVERSITY   (United States)

^c Depto de Matemática Aplicada   (Spain)

Author keywords

Difference equations; Global asymptotic stability; Halanay inequality

Indexed keywords

ASYMPTOTIC STABILITY; DIFFERENCE EQUATIONS; MATHEMATICAL MODELS; THEOREM PROVING;

GLOBAL ASYMPTOTIC STABILITY;

NONLINEAR EQUATIONS;

EID: 0142043484     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2003.07.013     Document Type: Article

References (11)

1. Elaydi S.N. An Introduction to Difference Equations. 1996;Springer, New York.
2. n-1} with a period 3 parameter Faria T., Freitas P. Functional Differential and Difference Equations, Fields Institute Communications series. 2001;161-180 American Mathematical Society, Providence, RI.
3. Halanay A. Differential Equations: Stability, Oscillations, Time Lags. 1966;Academic Press, New York.
4. Ivanov A., Liz E., Trofimchuk S. Halanay inequality, Yorke 3/2 stability criterion, and differential equations with maxima. Tohoku Math. J. 54:2002;277-295.
5. Kuang Y. Delay Differential Equations with Applications in Population Dynamics. 1993;Academic Press, New York.
6. Liu Z.R., Xie H.M., Zhu Z.X., Lu Q.H. The strange attractor of the Lozi mapping. Int. J. Bifur. Chaos. 2:1992;831-839.
7. Liz E., Ferreiro J.B. A note on the global stability of generalized difference equations. Appl. Math. Lett. 15:2002;655-659.
8. Liz E., Trofimchuk S. Existence and stability of almost periodic solutions for quasilinear delay systems and the Halanay inequality. J. Math. Anal. Appl. 248:2000;625-644.
9. M. Misiurewicz, Strange attractor for the Lozi mapping, in: Nonlinear Dynamics, Ann. N. Y. Acad. Sci. 357 (1980) 348-358.
10. Mohamad S., Gopalsamy K. Continuous and discrete Halanay-type inequalities. Bull. Aust. Math. Soc. 61:2000;371-385.
11. Pinto M., Trofimchuk S. Stability and existence of multiple periodic solutions for a quasilinear differential equation with maxima. Proc. Roy. Soc. Edinburgh Sect. A. 130:2000;1103-1118.