3 problems

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…

Assume that $f_a(u)=u(1-u)(u-a)$ with $0<a<1/2$. Let $\mathcal{K}$ satisfy the stated hypotheses with normalized second moment … Let $\mathcal{R}_j$, $j=1,\ldots,5$, be the regions…

Assume that $\mathcal{K}(x)=\mathrm{e}^{-|x|}/2$ and that $f_a(u)=u(1-u)(u-a)$ with $0<a<1/2$. Let $(a,d)\in \mathcal{R}_2\cup\mathcal{R}_3$ such that $0<\ell_1^*<\infty$ is well d…