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2015 | OriginalPaper | Chapter

1. Introduction, Notation, and Background

Authors : Sigrun Bodine, Donald A. Lutz

Published in: Asymptotic Integration of Differential and Difference Equations

Publisher: Springer International Publishing

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Abstract

This book is concerned with the problem of determining the asymptotic behavior of solutions of non-autonomous systems of linear differential and linear difference equations. It has been observed from the work by Poincaré and Perron that there is a very close and symbiotic relationship between many results for differential and difference equations, and we wish to further demonstrate this by treating the asymptotic theories here in parallel. In Chaps. 2, 4, 6, and 8 we will discuss topics related to asymptotic behavior of solutions of differential equations, and in Chaps. 3, 5, 7, and 9 some corresponding results for difference equations. In Chap. 10 we will show how some of these results can be simultaneously treated within the framework of so-called dynamic equations on time scales.

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next chapter Asymptotic Integration for Differential Systems
Literature
1.
R.P. Agarwal, Difference Equations and Inequalities: Theory, Methods, and Applications (Marcel Dekker, New York, 2000)
3.
W. Balser, Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations. Universitext (Springer, New York, 2000)MATH
4.
R.G. Bartle, A Modern Theory of Integration. Graduate Studies in Mathematics, vol. 32 (American Mathematical Society, Providence, 2001)
5.
P.M. Batchelder, An Introduction to Linear Difference Equations (Dover Publications Inc., New York, 1967)
20.
S. Bodine, R.J. Sacker, A new approach to asymptotic diagonalization of linear differential systems. J. Dyn. Differ. Equ. 12, 229–245 (2000)CrossRefMATHMathSciNet
42.
E.A. Coddington, N. Levinson, Theory of Ordinary Differential Equations (McGraw-Hill Book Company Inc., New York/Toronto/London, 1955)MATH
43.
W.A. Coppel, Stability and Asymptotic Behavior of Differential Equations (D. C. Heath and Co., Boston, 1965)MATH
53.
M.S.P. Eastham, The Asymptotic Solution of Linear Differential Systems. Applications of the Levinson Theorem (Oxford University Press, Oxford, 1989)
55.
72.
P. Hartman, Ordinary Differential Equations (Birkhäuser, Boston, 1982)MATH
77.
P.F. Hsieh, Y. Sibuya, Basic Theory of Ordinary Differential Equations (Springer, New York, 1999)CrossRefMATH
80.
P.F. Hsieh, F. Xie, On asymptotic diagonalization of linear ordinary differential equations. Dyn. Contin. Discrete Impuls. Syst. 4, 351–377 (1998)MATHMathSciNet
82.
G.K. Immink, Asymptotics of Analytic Difference Equations. Lecture Notes in Mathematics, vol. 1085 (Springer, Berlin, 1984)
86.
C. Jordan, Calculus of Finite Differences (Chelsea Publishing Co., New York, 1965)MATH
87.
W.B. Jurkat, Meromorphe Differentialgleichungen. Lecture Notes in Mathematics, vol. 637 (Springer, Berlin, 1978)
88.
W. Kelley, A.C. Peterson, Difference Equations: An Introduction with Applications (Harcourt/Academic, San Diego, 2001)
95.
M. Kohno, Global Analysis in Linear Differential Equations. Mathematics and Its Applications, vol. 471 (Kluwer Academic Publishers, Dordrecht, 1999)
99.
V. Lakshmikantham, D. Trigiante, Theory of Difference Equations: Numerical Methods and Applications (Marcel Dekker, New York, 2002)CrossRef
100.
109.
H. Meschkowski, Differenzengleichungen. Studia Mathematica, Bd. XIV (Vandenhoeck & Ruprecht, Göttingen, 1959)
113.
P.G. Nevai, Orthogonal Polynomials. Memoirs of the American Mathematical Society, vol. 18 (American Mathematical Society, Providence, 1979)
114.
N.E. Nörlund, Leçons sur les séries d’interpolation (Gautiers-Villars, Paris, 1926)MATH
116.
F.W.J. Olver, Asymptotics and Special Functions. Computer Science and Applied Mathematics (Academic, New York/London, 1974)
Metadata
Title
Introduction, Notation, and Background
Authors
Sigrun Bodine
Donald A. Lutz
Copyright Year
2015
Book
Asymptotic Integration of Differential and Difference Equations

Print ISBN: 978-3-319-18247-6

Electronic ISBN: 978-3-319-18248-3

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-18248-3_1

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