6 problems

Homogeneous Lyapunov converse conjecture. For homogeneous vector fields, asymptotic stability implies existence of a polynomial Lyapunov function. Equivalently, existence of a homo…

Homogeneous cubic focal-value conjecture. If no points of $X_5-X_6$ are found in the stated random search, then

Zoladek's conjecture. All cubic systems with stable solutions near the origin are either of Darboux type or rationally reversible.

Composition condition conjecture. The sufficient condition given in Theorem 1 is also necessary for a polynomial Abel differential equation to have a center on $[a,b]$.

Let $n$ be the degree of the polynomial differential equation under consideration, and suppose the equation has real coefficient functions $P_i(t)$. The preceding results show that…

Consider a polynomial differential equation with polynomial coefficients $P_i(t)$, including the constant and linear coefficients $P_0$ and $P_1$. No-centers conjecture. Equations…