Limit cycle's uniqueness for second order O.D.E.'s polynomial in $\dot{x}$

Abstract

We prove a uniqueness result for limit cycles of the second order ODE $\ddot{x}+{\sum }_{j=1}^J{f}_j(x){\dot{x}}^j+g(x)=0$. We extend a uniqueness result proved in \cite{CRV}. The main tool applied is an extension of Massera theorem proved in \cite{GS}.

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Cited by in corpus (1)

• On the uniqueness of limit cycles for Liénard equation: the legacy of G. Sansone