4 problems

Consider the Liénard system … where $F(x)$ is a polynomial of odd degree $m$, and let $N$ be determined by $m=2N+1$ or $m=2N+2$. Lins–Pugh–de Melo conjecture. The system has at mos…

Let $a_1$ and $a_2$ be parameters satisfying … In this parameter region, the system has no small limit cycles and at most four large limit cycles. Two-large-limit-cycle conjecture.…

Consider system … is exactly $3$. This conjecture is motivated by the system's symmetry and by numerical simulations showing one large limit cycle when there are two small limit cy…

Let the classical Liénard system be … where $F(x)=\sum_{i=0}^{n}a_i x^i$ is a polynomial and $[\cdot]$ denotes the integer function. Liénard's conjecture. The classical Liénard sys…