Existence, uniqueness, and stability of oscillations in differential equations with asymmetric nonlinearities. (English) Zbl 0725.34042

Conditions for the existence, uniqueness and asymptotic stability of periodic solutions are obtained for 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, a necessary and sufficient condition is given.


34C25 Periodic solutions to ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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