11 problems

Let $x$ be a slowly oscillating periodic solution (SOPS) of Wright's equation … with parameter $\alpha$ and period length $L(\alpha)$. Monotonicity conjecture. The period length of…

Periodic-solution conjecture. Under these assumptions, system $$ has a nontrivial slowly oscillating periodic solution.

Let … with parameter $\alpha>\tfrac{\pi}{2}$. A slowly oscillating periodic solution (SOPS) is a periodic solution $y(t)$ for which, up to time translation, there exist…

Consider an ODE of the form of equation with a bistable function $f(y)$. Five-solution conjecture. Such an ODE has at most five $1$-periodic solutions. This conjecture concerns the…

Periodic-solution conjecture. If all solutions are uniform-bounded and uniform ultimate-bounded, then there exists a nonzero periodic solution with period $T$, which need not be un…

Altshuller multiplier conjecture. If such a multiplier exists, then there exists a nonzero periodic solution with period $T$, which need not be unique or attracting.

Reducible-tree conjecture. The infinite reducible tree and its rescalings according to the relevant scaling provide an effective description for the structure of time-periodic solu…

Asymptotic label conjecture. There exists an index $j\notin I$ such that

Let $\alpha>\tfrac{\pi}{2}$, and consider the family of slowly oscillating periodic solutions (SOPS) of Wright's equation … An isola is a connected component of the SOPS family tha…

Let $z_{n+1}=\frac{\alpha+\beta z_{n-k}}{\gamma-z_n}$ be the complex rational delay difference equation, where $k$ is the delay and $p$ denotes the period of a periodic solution. E…

Let $z_{n+1}=\frac{\alpha+\beta z_{n-k}}{\gamma-z_n}$ be the complex rational delay difference equation, with parameters $\alpha$, $\beta$, $\gamma$ and delay $k$. A period $p$ is…