This is a preview of subscription content, log in via an institution to check access.
References
D. A. Flanders andJ. J. Stoker, The limit case of relaxation oscillations, Studies in non-linear vibration theory, New York University, 1946.
K. O. Friedrichs andW. R. Wasow, Singular perturbations of non-linear oscillations, Duke Math Journal, 13, 367–381 (1946).
N. Levinson, Perturbations of discontinuous solutions of non-linear systems of differential equations, Proc. Nat. Acad. of Sciences, 33, 214–218 (1947).
M. Nagumo, Über das Verhalten des Integrals von λy″+f(x, y, y′, λ)=0 für λ→0. Proc. Phys. Math. Soc., Japan 21, 529–534 (1939).
A. Tihonov, On the dependence of the solutions of differential equations on a small parameter. Mat. Sbornik N. S. 22, 193–204 (1948).
I. M. Volk, A generalization of the method of small parameter in the theory of non-linear oscillations of non-autonomous systems, C. R. (Doklady) Acad. Sci. U.S.S.R., 51, 437–440 (1946).
Author information
Authors and Affiliations
Additional information
John Simon Guggenheim Memorial Fellow on leave from the Massachusetts Institute of Technology.
Rights and permissions
About this article
Cite this article
Levinson, N. Perturbations of discontinuous solutions of non-linear systems of differential equations. Acta Math. 82, 71–106 (1950). https://doi.org/10.1007/BF02398275
Issue Date:
DOI: https://doi.org/10.1007/BF02398275