This is a preview of subscription content, log in via an institution to check access.
References
H. A. Antosiewicz, On non-linear differential equations of the second order with integrable forcing term,J. London Math. Soc. 30 (1955), 64–67.
E. A. Coddington andN. Levinson,Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955.
C. V. Coffman andD. F. Ullrich, On the continuation of solutions of a certain nonlinear differential equation,Monatsh. Math. 71 (1967), 385–392.
J. P. LaSalle andS. Lefschetz,Stability by Liapunov's Direct Method with Applications, Academic Press, New York, 1961.
J. S. Muldowney, On Liapunov's direct method,Rocky Mountain J. Math. 1 (1971), 469–482.
J. S. Muldowney, On an inequality of Peano,Canadian Math. Bull. (to appear).
M. Nagumo, Ueber die Lage der Integralkurven gewöhnlicher Differentialgleichungen,Proc. Phys.-Math. Soc. Japan 24 (1942), 551–559.
I. P. Natanson,Theory of Functions of a Real Variable, Ungar, New York, 1961.
C. M. Petty andG. Leitmann, A boundedness theorem for a nonlinear nonautonomous system,Monatsh. Math. 68 (1964), 46–51.
G. P. Szegö andG. Treccani, Non-continuous Liapunov functions,Ann. di Mat. Pura ed Appl. 82 (1969), 1–15.
J. A. Yorke, Differential inequalities and non-lipschitz scalar functions,Math. Systems Theory 4 (1970), 140–153.
T. Yoshizawa,Stability Theory by Liapunov's Second Method, The Mathematical Society of Japan, Tokyo, 1966.
Author information
Authors and Affiliations
Additional information
This research was supported by Defence Research Board of Canada Grant DRB-9540-28. Theorem 2 was presented in a contributed paper to the U.S.-Japan Seminar on Ordinary Differential and Functional Equations, Kyoto, Japan, September, 1971.
Rights and permissions
About this article
Cite this article
Muldowney, J.S. Discontinuous scalar functions and ordinary differential equations. Math. Systems Theory 8, 45–54 (1974). https://doi.org/10.1007/BF01761706
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01761706