Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Asymptotically constant linear systems


Author: Horst Behncke
Journal: Proc. Amer. Math. Soc. 138 (2010), 1387-1393
MSC (2000): Primary 34E10
DOI: https://doi.org/10.1090/S0002-9939-09-10146-6
Published electronically: October 28, 2009
MathSciNet review: 2578530
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The asymptotic integration of a linear system of differential equations $ y'(t) = (A(t) + R (t)) y(t)$ on the half line is investigated when $ A$ is almost constant with distinct eigenvalues. The difference equation analogue of this equation is also considered.


References [Enhancements On Off] (What's this?)

  • 1. H. Behncke: Spectral Theory of Higher Order Differential Operators. Proc. London Math. Soc. (3), 92 (2006), 139-160. MR 2192387 (2007b:47109)
  • 2. H. Behncke, D.B. Hinton: Eigenfunctions, Deficiency Indices and Spectra of Odd-Order Differential Operators, Proc. London Math. Soc. (3), 97 (2008), 425-449. MR 2439668 (2009g:34216)
  • 3. H. Behncke: The Remainder in Asymptotic Integration, Proc. Amer. Math. Soc., 136 (2008), 3231-3238. MR 2407088 (2009c:34117)
  • 4. Z. Benzaid, D. A. Lutz: Asymptotic Representation of Solutions of Perturbed Systems of Linear Difference Equations, Stud. Appl. Math., 77 (1987), 195-221. MR 1002291 (90f:39003)
  • 5. S. Bodine: A Dynamical Systems Result on Asymptotic Integration of Linear Differential Systems, J. Diff. Eqn., 187 (2003), 1-22. MR 1946543 (2003m:34109)
  • 6. M. S. P. Eastham: The Asymptotic Solution of Linear Differential Systems, London Math. Soc. Monographs, The Clarendon Press, Oxford University Press, New York, 1989. MR 1006434 (91d:34001)
  • 7. N. Ju, S. Wiggins: On Roughness of Exponential Dichotomy, J. Math. Anal. Appl., 262 (2001), 39-49. MR 1857213 (2002g:34100)
  • 8. N. Levinson: The Asymptotic Nature of Solutions of Linear Systems of Differential Equations, Duke Math. J., 15 (1948), 111-126. MR 0024538 (9:509h)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 34E10

Retrieve articles in all journals with MSC (2000): 34E10


Additional Information

Horst Behncke
Affiliation: Fachbereich Mathematik/Informatik, Universität Osnabrück, 49069 Osnabrück, Germany

DOI: https://doi.org/10.1090/S0002-9939-09-10146-6
Received by editor(s): May 13, 2009
Received by editor(s) in revised form: July 31, 2009
Published electronically: October 28, 2009
Communicated by: Yingfei Yi
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society