Existence, uniqueness, and stability of oscillations in differential equations with asymmetric nonlinearities

Lazer, A. C.; McKenna, P. J.

doi:10.1090/S0002-9947-1989-0979963-1

Existence, uniqueness, and stability of oscillations in differential equations with asymmetric nonlinearities
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by A. C. Lazer and P. J. McKenna

Trans. Amer. Math. Soc. 315 (1989), 721-739

DOI: https://doi.org/10.1090/S0002-9947-1989-0979963-1

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Abstract:

We give conditions for the existence, uniqueness, and asymptotic stability of periodic solutions of a second-order differential equation with piecewise linear restoring and $2\pi$-periodic forcing where the range of the derivative of the restoring term possibly contains the square of an integer. With suitable restrictions on the restoring and forcing in the undamped case, we give a necessary and sufficient condition.

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