6 problems

Let $g(x)=x$, and let $f(x)$ be a polynomial of degree $n\geq 1$. Consider the generalized Liénard equation … Here, $[r]$ denotes the integer part of $r$. Lins–de Melo–Pugh conject…

Consider the system … with the parameter normalized to $\epsilon=1$ by a linear change of coordinates. Two-limit-cycle conjecture. The resulting system for $\epsilon=1$ has at most…

Nonexistence conjecture. There is no global analytic first integral for this system on $\mathbb{R}^2$. The claim concerns global analytic integrability of planar Liénard systems; t…

Global attraction conjecture. The attractor at the origin is also global.

Smale's conjecture. There exists an integer $n$ and a real $C$ such that the number of limit cycles of this equation is not bigger than

Lins Neto–de Melo–Pugh conjecture. The number of limit cycles of this equation is not bigger than