3 problems

Regularity conjecture. If $h\in C[0,1]$ or $h\in L^1(0,1)$, then the solution $u$ belongs to $C^1_{2-\alpha}[0,1]$. Moreover, if $h\in C(0,1]$ satisfies $(H)$, then the solution…

Singular-point conjecture. There exist singular points in the trajectory if and only if

Audounet–Matignon–Montseny conjecture. The local stability of $x^{*}=0$ is governed by the global stability of the linearized system as follows: (i) $x^{*}=0$ is locally asymptotic…