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Large scale oscillatory behaviour in loaded asymmetric systems. (English) Zbl 0633.34037

The authors study 2π-periodic solutions of “asymmetric” nonlinear differential equations of the form u '' +g(u)=s(1+ϵh(t)), where s is a constant, ϵ a small parameter, h(t+2π)=h(t) and g ' (+)g ' (-). Depending on g(u) there exist many such solutions close to s.

{Reviewer’s remark: These results are closely related to H. Ehrmann [Z. Angew. Math. Mech. 35, 326-327 (1955; Zbl 0065.074)].}

Reviewer: E.Brommundt

34C25Periodic solutions of ODE
34C15Nonlinear oscillations, coupled oscillators (ODE)