Dynamic behavior from asymptotic expansions
Authors:
Jack K. Hale and Luiz Carlos Pavlu
Journal:
Quart. Appl. Math. 41 (1983), 161-168
MSC:
Primary 34C25; Secondary 34C27
DOI:
https://doi.org/10.1090/qam/700669
MathSciNet review:
700669
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: The purpose of this paper is to discuss stability properties of solutions of periodic and almost-periodic differential equations containing a small parameter. The existence of the solution can be obtained in the first approximation but the stability only after $k$ approximations. We obtain the results using asymptotic expansions, higher-order averaging and the concept of exponential hyperbolicity of order $k$.
- W. A. Coppel, Dichotomies in stability theory, Lecture Notes in Mathematics, Vol. 629, Springer-Verlag, Berlin-New York, 1978. MR 0481196
- W. A. Coppel, Dichotomies and reducibility, J. Differential Equations 3 (1967), 500–521. MR 223651, DOI https://doi.org/10.1016/0022-0396%2867%2990014-9
- A. M. Fink, Almost periodic differential equations, Lecture Notes in Mathematics, Vol. 377, Springer-Verlag, Berlin-New York, 1974. MR 0460799
- Jack K. Hale, Ordinary differential equations, 2nd ed., Robert E. Krieger Publishing Co., Inc., Huntington, N.Y., 1980. MR 587488
- M. A. Krasnosel′skiĭ, V. Sh. Burd, and Yu. S. Kolesov, Nonlinear almost periodic oscillations, Halsted Press [A division of John Wiley & Sons], New York-Toronto, Ont.; Israel Program for Scientific Translations, Jerusalem-London, 1973. Translated from the Russian by A. Libin; Translation edited by D. Louvish. MR 0344595
- J. A. Murdock, Some mathematical aspects of spin-orbit resonance, Celestial Mech. 18 (1978), no. 3, 237–253. MR 513723, DOI https://doi.org/10.1007/BF01230164
J. A. Murdock and C. Robinson, Qualitative dynamics from asymptotic expansions—local theory, J. Diff. Eqs. 36, 425–441 (1980)
W. A. Coppel, Dichotomies in stability theory, Springer-Verlag, 1978
W. A. Coppel, Dichotomies and reducibility, J. Diff. Eqs. 3, 500–521 (1973)
A. M. Fink, Almost periodic differential equations, Springer-Verlag, 1974
J. K. Hale, Ordinary differential equations, 2nd ed., Robert E. Krieger Publishing Co., New York, 1980
M. A. Krasnosels’ki, V. S. Burd and Y. S. Kolesov, Nonlinear almost periodic oscillations, John Wiley & Sons, New York, 1973
J. A. Murdock, Some mathematical aspects of spin orbit resonance, Cel. Mech. 8, 237–253 (1978)
J. A. Murdock and C. Robinson, Qualitative dynamics from asymptotic expansions—local theory, J. Diff. Eqs. 36, 425–441 (1980)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
34C25,
34C27
Retrieve articles in all journals
with MSC:
34C25,
34C27
Additional Information
Article copyright:
© Copyright 1983
American Mathematical Society
