Perron-type stability theorems for neutral equations

Nonlinear Analysis, Theory, Methods and Applications

Volumn 55, Issue 3, 2003, Pages 285-297

  Burton, T A ^a  

^a Northwest Research Institute   (United States)

Author keywords

Fixed points; Neutral equations; Perron theorem; Stability

Indexed keywords

ASYMPTOTIC STABILITY; NONLINEAR EQUATIONS; SET THEORY; THEOREM PROVING;

NEUTRAL EQUATIONS;

DIFFERENTIAL EQUATIONS;

EID: 0041387376     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(03)00240-2     Document Type: Article

References (11)

1. Bellman R. Stability Theory of Differential Equations. 1953;McGraw-Hill, New York.
2. Burton T.A. Liapunov functionals, fixed points, and stability by Krasnoselskii's theorem. Nonlinear Stud. 9:2002;181-190.
3. Burton T.A., Furumochi Tetsuo Fixed points and problems in stability theory. Dyn. Systems Appl. 10:2001;89-116.
4. Burton T.A., Tetsuo Furumochi Krasnoselskii's fixed point theorem and stability. Nonlinear Anal. 49:2002;445-454.
5. Krasnoselskii M.A. Some problems of nonlinear analysis. Amer. Math. Soc. Transl. (2). 10:1958;345-409.
6. V. Lakshmikantham, S. Leela, Differential and Integral Inequalities, Vol. I, Academic Press, New York, 1969.
7. Perron O. Die stabilitatsfrage bei differentialgleichungen. Math. Z. 32:1930;703-728.
8. I.A. Rus, Picard Operators and Applications, Babes-Bolyai University, Cluj-Napoca, Romania, 1996.
9. Saito Seiji Global stability of solutions for quasilinear ordinary differential systems. Math. Japonica. 34:1989;821-929.
10. M.-A. Serban, Global asymptotic stability for some difference equations via fixed point technique, Seminar on Fixed Point Theory, Vol. 2, Cluj-Napoca, 2002, pp. 87-96.
11. Smart D.R. Fixed Point Theorems. 1974;Cambridge University Press, Cambridge.