Asymptotically autonomous multivalued differential equations
Author:
James P. Foti
Journal:
Trans. Amer. Math. Soc. 221 (1976), 449-452
MSC:
Primary 34D05
DOI:
https://doi.org/10.1090/S0002-9947-1976-0435524-5
MathSciNet review:
0435524
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: The asymptotic behavior of solutions of the perturbed autonomous multivalued differential equation is examined in relation to the behavior of solutions of the autonomous equation
assuming that all solutions of the latter approach zero as t approaches
.
- [1] H. A. Antosiewicz, Stable systems of differential equations with integrable perturbation term, J. London Math. Soc. 31 (1956), 208-212. MR 18, 42. MR 0079178 (18:42c)
- [2] Fred Brauer and Aaron Strauss, Perturbations of nonlinear systems of differential equations. III, J. Math. Anal. Appl. 31 (1970), 37-48. MR 41 #3919. MR 0259277 (41:3919)
- [3] L. Cesari, Asymptotic behavior and stability problems in ordinary differential equations, Ergebnisse der Math. und ihrer Grenzgebiete, N. F., Band 16, Academic Press, New York; Springer-Verlag, Berlin, 1963. MR 27 #1661.
- [4] E. A. Coddington and N. Levinson, Theory of ordinary differential equations, McGraw-Hill, New York, 1955. MR 16, 1022. MR 0069338 (16:1022b)
- [5] A. Lasota and Aaron Strauss, Asymptotic behavior for differential equations which cannot be locally linearized, J. Differential Equations 10 (1971), 152-172. MR 43 #3570. MR 0277837 (43:3570)
- [6] S. Lefschetz, Differential equations: Geometric theory, 2nd ed., Pure and Appl. Math., vol. 6, Interscience, New York, 1963. MR 27 #3864. MR 0153903 (27:3864)
- [7] Aaron Strauss and James A. Yorke, On asymptotically autonomous differential equations, Math. Systems Theory 1 (1967), 175-182. MR 35 #4524. MR 0213666 (35:4524)
- [8] -, Perturbation theorems for ordinary differential equations, J. Differential Equations 3 (1967), 15-30. MR 34 #3029. MR 0203176 (34:3029)
- [9] -, Perturbing uniform asymptotically stable nonlinear systems, J. Differential Equations 6 (1969), 452-483. MR 40 #5998. MR 0252781 (40:5998)
- [10] T. Yoshizawa, Stability theory by Lyapunov's second method, Publ. Math. Soc. Japan, no. 9, Math. Soc. Japan, Tokyo, 1966. MR 34 #7896. MR 0208086 (34:7896)
Retrieve articles in Transactions of the American Mathematical Society with MSC: 34D05
Retrieve articles in all journals with MSC: 34D05
Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1976-0435524-5
Article copyright:
© Copyright 1976
American Mathematical Society