Available in electronic format
Available in print format
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

Asymptotically constant linear systems

Author(s): Horst Behncke
Journal: Proc. Amer. Math. Soc.
MSC (2000): Primary 34E10
Posted: October 28, 2009
Retrieve article in: PDF

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:

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: 10.1090/S0002-9939-09-10146-6
PII: S 0002-9939(09)10146-6
Received by editor(s): May 13, 2009,
Received by editor(s) in revised form: July 31, 2009
Posted: October 28, 2009
Communicated by: Yingfei Yi
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google