Rocky Mountain Journal of Mathematics

Asymptotic Integration Under Weak Dichotomies

Sigrun Bodine and D.A. Lutz

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Rocky Mountain J. Math. Volume 40, Number 1 (2010), 51-75.

First available in Project Euclid: 15 March 2010

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Differential equations perturbations dichotomy conditions asymptotic behavior difference equations


Bodine, Sigrun; Lutz, D.A. Asymptotic Integration Under Weak Dichotomies. Rocky Mountain J. Math. 40 (2010), no. 1, 51--75. doi:10.1216/RMJ-2010-40-1-51.

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  • H. Behncke and C. Remling, Asymptotic integration of linear differential equations, J. Math. Anal. Appl. 210 (1997), 585-597.
  • Z. Benzaid and D.A. Lutz, Asymptotic representation of solutions of perturbed systems of linear difference equations, Studies Appl. Math. 77 (1987), 195-221.
  • S. Bodine and D.A. Lutz, On asymptotic equivalence of perturbed linear systems of differential and difference equations, J. Math. Anal. Appl. 326 (2007), 1174-1189.
  • --------, Asymptotic solutions and error estimates for linear systems of difference and differential equations, J. Math. Anal. Appl. 290 (2004), 343-362.
  • K. Chiba and T. Kimura, On the asymptotic behavior of solutions of a system of linear ordinary differential equations, Comment. Math. Univ. St. Paul. 18 (1970), 61-80.
  • W.A. Coppel, Stability and asymptotic behavior of differential equations, Heath, Boston, 1965.
  • A. Devinatz, An example where Levinson's theorem fails (without assuming a dichotomy condition), private communication.
  • M.S.P. Eastham, The asymptotic solution of linear differential systems. Applications of the Levinson theorem, Oxford University Press, New York, 1989.
  • H. Gingold, Almost diagonal systems in asymptotic integration, Proc. Edinburgh Math. Soc. 28 (1985), 143-158.
  • W.A. Harris and D.A. Lutz, A unified theory of asymptotic integration, J. Math. Anal. Appl. 57 (1977), 571-586.
  • P.F. Hsieh and F. Xie, On asymptotic diagonalization of linear ordinary differential equations, Dynamic Continuous Discrete Impulsive Systems 4 (1998), 351-377.
  • N. Levinson, The asymptotic nature of solutions of linear systems to differential equations, Duke Math. J. 15 (1948), 111-126.