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Perturbations of discontinuous solutions of non-linear systems of differential equations. (English) Zbl 0039.31404


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[1] D. A. Flanders andJ. J. Stoker, The limit case of relaxation oscillations, Studies in non-linear vibration theory, New York University, 1946. · Zbl 0061.19315
[2] K. O. Friedrichs andW. R. Wasow, Singular perturbations of non-linear oscillations, Duke Math Journal, 13, 367–381 (1946). · Zbl 0061.19509 · doi:10.1215/S0012-7094-46-01331-2
[3] N. Levinson, Perturbations of discontinuous solutions of non-linear systems of differential equations, Proc. Nat. Acad. of Sciences, 33, 214–218 (1947). · Zbl 0029.35803 · doi:10.1073/pnas.33.7.214
[4] M. Nagumo, Über das Verhalten des Integrals von {\(\lambda\)}y”+f(x, y, y’, {\(\lambda\)})=0 für {\(\lambda\)}. Proc. Phys. Math. Soc., Japan 21, 529–534 (1939). · Zbl 0022.13703
[5] A. Tihonov, On the dependence of the solutions of differential equations on a small parameter. Mat. Sbornik N. S. 22, 193–204 (1948).
[6] 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). · Zbl 0061.18906
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