Abstract
AbstractWe study the oscillator $$\ddot{x} + n^2 x + h(x) = p(t)$$
x
¨
+
n
2
x
+
h
(
x
)
=
p
(
t
)
, where h is a piecewise linear saturation function and p is a continuous $$2\pi $$
2
π
-periodic forcing. It is shown that there is recurrence if and only if p satisfies the Lazer–Leach condition. This condition relates the n-th Fourier coefficient of p(t) with the maximum of h and was first introduced to characterize the existence of periodic solutions.
Funder
Deutsche Forschungsgemeinschaft
Universität zu Köln
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Nuclear and High Energy Physics,Statistical and Nonlinear Physics
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