References
Cesari, L., Asymptotic Behavior and Stability Problems in Ordinary Differential Equations, 2nd. ed. New York: Academic Press 1963.
Coddington, E. A.,& N. Levinson, Theory of Ordinary Differential Equations. New York: McGraw-Hill 1955.
Hochstadt, H., Differential Equations — A Modern Approach. Holt, Rinehart & Winston 1964.
Eckweiler, H.J., Nonlinear Differential Equations of the Van der Pol type with a Variety of Periodic Solutions, Studies in Nonlinear Vibration Theory. Institute for Mathematics and Mechanics, New York University, 1946.
Stoker, J.J., Nonlinear Vibrations. New York: Interscience Publishers 1950.
Magnus, W.,& F. Oberhettinger, Formulas and Theorems for the Special Functions of Mathematical Physics. New York: Chelsea Pub. Co. 1949.
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Communicated by W. Magnus
This research was supported by the National Science Foundation under grant GP 4171.
This research was submitted to the Faculty of the Polytechnic Institute of Brooklyn in partial fulfillment of the requirements for the degree Doctor of Philosophy, awarded to B.H. Stephan in 1966.
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Hochstadt, H., Stephan, B.H. On the limit cycles of \(\ddot x + \mu \sin \dot x + x = 0\) . Arch. Rational Mech. Anal. 23, 369–379 (1967). https://doi.org/10.1007/BF00276780
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DOI: https://doi.org/10.1007/BF00276780