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.
2004
1
Sabatini, Marco
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]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/74060
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