Geodesic
Non-monotone period functions for impact oscillators
Electronic journal of differential equations, Tome 2008 (2008)
The existence of non-monotone period functions for differential equations of the form

$ \ddot{x}+f(x)+\gamma H(x)g(x)=0 $

is proved for large

$ \ddot{x}+\sin x +\gamma H(x) x^{3/2}=0, $

which models the conservative dimensionless impact pendulum utilizing Hertzian contact during impact with a barrier at the downward vertical position.
Classification : 34C15, 34C25, 37N15
Keywords: period function, impact oscillator 
@article{EJDE_2008__2008__a6,
     author = {Chicone,  Carmen and Felts,  Kenny},
     title = {Non-monotone period functions for impact oscillators},
     journal = {Electronic journal of differential equations},
     year = {2008},
     volume = {2008},
     zbl = {1173.34031},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a6/}
}
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Chicone,  Carmen; Felts,  Kenny. Non-monotone period functions for impact oscillators. Electronic journal of differential equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a6/