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

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

2010-11-08

arxiv.org/abs/1011.1785v1

Mathematics

Classical Analysis and ODEs

2 figures

Scientific paper

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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