Fixed points, stability, and exact linearization

Nonlinear Analysis, Theory, Methods and Applications

Volumn 61, Issue 5, 2005, Pages 857-870

  Burton, T A ^a  

^a Northwest Research Institute   (United States)

Author keywords

Asymptotic stability; Contraction mappings; Second order delay equations

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; COMPUTATIONAL METHODS; CONFORMAL MAPPING; INTEGRAL EQUATIONS; LINEAR EQUATIONS; LYAPUNOV METHODS; NONLINEAR EQUATIONS;

CONTRACTION MAPPINGS; LIPSCHITZ CONSTANT; SCALAR EQUATIONS; SECOND-ORDER DELAY EQUATIONS;

LINEARIZATION;

EID: 14944366448     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2005.01.079     Document Type: Article

References (15)

1. R.J. Ballieu, and K. Peiffer Attractivity of the origin for the equation x ″ + f (t, x, x ′) | x ′ | α x ′ + g (x) = 0 J. Math. Anal. Appl. 65 1978 321 332
2. T.A. Burton Stability and Periodic Solutions of Ordinary and Functional Differential Equations 1985 Academic Press Orlando
3. T.A. Burton Stability by fixed point theory or Liapunov theory a comparison Fixed Point Theory 4 2003 15 32
4. T.A. Burton Fixed points and stability of a nonconvolution equation Proc. Am. Math. Soc. 132 2004 3679 3687
5. T.A. Burton, and J.W. Hooker On solutions of differential equations tending to zero J. Reine Angew. Math. 267 1974 151 165
6. L. Hatvani Nonlinear oscillation with large damping Dyn. Syst. Appl. 1 1992 257 270
7. L. Hatvani Integral conditions on the asymptotic stability for the damped linear oscillator with small damping Proc. Am. Math. Soc. 124 1996 415 422
8. L. Hatvani, and T. Krisztin Necessary and sufficient conditions for intermittent stabilization of linear oscillators by large damping Differential Integral Equations 10 1997 265 272
9. L. Hatvani, T. Krisztin, and V. Totik A necessary and sufficient condition for the asymptotic stability of the damped oscillator J. Differential Equations 119 1995 209 223
10. L. Hatvani, and V. Totik Asymptotic stability of the equilibrium of the damped oscillator Differential Integral Equations 6 1993 835 848
11. J.J. Levin, and J.A. Nohel Global asymptotic stability for nonlinear systems of differential equations Arch. Rational Mech. Anal. 5 1960 194 211
12. P. Pucci, and J. Serrin Asymptotic stability for intermittently controlled nonlinear oscillators SIAM J. Math. Anal. 25 1994 815 835
13. R.A. Smith Asymptotic stability of x ″ + a (t) x ′ + x = 0 Quart. J. Math. Oxford Ser. 12 2 1961 123 126
14. L.H. Thurston, and J.S.W. Wong On global asymptotic stability of certain second order differential equations with integrable forcing terms SIAM J. Appl. Math. 24 1973 50 61
15. B. Zhang On the retarded Liénard equation Proc. Am. Math. Soc. 115 1992 779 785