Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and uniqueness of limit cycles in a class of second order
  ODE's with inseparable mixed terms   We prove a uniqueness result for limit cycles of the second order ODE $\ddot
x + \dot x \phi(x,\dot x) + g(x) = 0$. Under mild additional conditions, we
show that such a limit cycle attracts every non-constant solution. As a special
case, we prove limit cycle's uniqueness for an ODE studied in \cite{ETA} as a
model of pedestrians' walk. This paper is an extension to equations with a
non-linear $g(x)$ of the results presented in \cite{S}.

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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci