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

The authors study \(2\pi\)-periodic solutions of “asymmetric” nonlinear differential equations of the form \(u''+g(u)=s(1+\epsilon h(t)),\) where s is a constant, \(\epsilon\) a small parameter, \(h(t+2\pi)=h(t)\) and \(g'(+\infty)\neq g'(-\infty)\). 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


34C25 Periodic solutions to ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations


Zbl 0065.074
Full Text: DOI Numdam EuDML


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