Stability in neutral nonlinear differential equations with functional delays using fixed-point theory

Mathematical and Computer Modelling

Volumn 40, Issue 7-8, 2004, Pages 691-700

  Raffoul, Y N ^a  

^a UNIVERSITY OF DAYTON   (United States)

Author keywords

Asymptotic stability; Contraction mapping; Integral equation; Nonlinear neutral differential equation

Indexed keywords

FUNCTIONS; STABILITY; THEOREM PROVING;

FIXED-POINT THEOREMS; FUNCTIONAL DELAYS; NONLINEAR DIFFERENTIAL EQUATIONS;

NONLINEAR EQUATIONS;

EID: 14944338681     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2004.10.001     Document Type: Article

References (16)

1. L. Hatvani Annulus arguments in the stability theory for functional differential equations Differential and Integral Equations 10 1997 975 1002
2. Y.N. Raffoul Periodic solutions in neutral nonlinear differential equations with functional delay Electron. J. Differential Equations 102 7 2003 1 7
3. T.A. Burton, and T. Furumochi Fixed points and problems in stability theory Dynamical Systems and Appl. 10 2001 89 116
4. J. Hale Theory of Functional Differential Equations 1977 Springer New York
5. T.A. Burton Volterra Integral and Differential Equations 1983 Academic Press New York
6. T.A. Burton Stability and Periodic Solutions of Ordinary and Functional Differential Equations 1985 Academic Press New York
7. T. Yohizawa Stability Theory by Liapunov's Second Method Tokyo Math. Soc., Japan 1966
8. T.A. Burton, and L. Hatvani Stability theorems for non-autonomous functional differential equations by Liapunov functionals Tohoku Math. J. 41 1989 295 306
9. Y. Hino, and S. Murakami Lecture Notes in Numerical and Applied Analysis Volume 15 1996 Kinokuniya New York 31 46
10. Y.N. Raffoul Uniform asymptotic stability in linear Volterra systems with nonlinear perturbation Int. J. Differ. Equ. Appl. 6 1 2002 19 28
11. B. Zhang Asymptotic criteria and integrability properties of the resolvent of Volterra and functional equations Funkcialaj Ekvacioj 40 1997 335 351
12. L.C. Becker Stability consideration for Volterra integro-differential equations Ph.D. Dissertation 1979 Southern Illinois University Tokyo
13. P. Eloe, and M. Islam Stability properties and integrability of the resolvent of linear Volterra equations Tohoku Math. J. 47 1995 263 269
14. P. Eloe, M. Islam, and B. Zhang Uniform asymptotic stability in linear Volterra integrodifferential equations with applications to delay systems Dynamic Systems and Applications 9 2000 331 334
15. Y. Hino, and S. Murakami Total stability and uniform asymptotic stability for linear Volterra equations J. London Math. Soc. 43 1991 305 312
16. M. Islam, and Y. Raffoul Stability properties of linear Volterra integrodifferential equations with nonlinear perturbation Communication of Applied Analysis 7 2-3 2003 405 416