We study the period function T of a center O of the title’s equation. A sufficient condition for the monotonicity of T, or for the isochronicity of O, is given. Such a condition is also necessary, when f and g are odd and analytic. In this case a characterization of isochronous centers is given. Some classes of plane systems equivalent to such equation are considered, including some Kukles’ systems.
On the period function of x'+f(x)x'^2+g(x)=0 / Sabatini, Marco. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 196:1(2004), pp. 151-168. [10.1016/S0022-0396(03)00067-6]
On the period function of x'+f(x)x'^2+g(x)=0
Sabatini, Marco
2004-01-01
Abstract
We study the period function T of a center O of the title’s equation. A sufficient condition for the monotonicity of T, or for the isochronicity of O, is given. Such a condition is also necessary, when f and g are odd and analytic. In this case a characterization of isochronous centers is given. Some classes of plane systems equivalent to such equation are considered, including some Kukles’ systems.File in questo prodotto:
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