9 problems

Spherically symmetric scattering conjecture. In the defocusing case ($\mu=+1$) we have $m_{0,\operatorname{rad}}=+\infty$, while in the focusing case ($\mu=-1$) we have…

Let $B_R\subset\mathbb{R}^N$ be the ball of radius $R$, let $2^*=\frac{2N}{N-2}$, and let $(u_k)_{k\geq 0}$ be radial solutions of the critical Lin–Ni–Takagi problem with exponent…

Let $\Lambda^*<\lambda_*<\Lambda_1$ and set $\beta_*=1$. Let $S_{1,\lambda,\beta}$ denote the class of radial sign-changing solutions with the index specified in the paper, and let…

Let $\chi>0$, $k\in(-N,0)$, and $m=2N/(2N+k)$ in dimension $N\geq1$. Assume that the initial datum $\rho_0\in{\mathcal Y}$ is radially symmetric. Global-existence-versus-blow-up co…

Let $N\geqslant 3$, let $i\geqslant 2$, and assume $2+oubles$?

Let $(\beta_1,\ldots,\beta_{k-1})$ be the configuration appearing in the $k$-layer limit problem of Theorem defining the corresponding multi-layer radial solution. Uniqueness conje…

Consider the radially symmetric biharmonic nonlinear heat equation … and let $L(t)$ and $r_{\max}(t)$ denote the ring similarity scale and radius. Let $v_B(t,x)$ be a singular peak…

Let $\psi$ be a singular standing-ring solution of the BNLS with $d>1$ and $\sigma>4$. Let $L(t)$ be the ring-region similarity scale, $r_{\max}(t)$ its radius, and $\psi_B$ the ring p…

Let $\psi$ be a singular standing-ring solution of the NLS equation with $d>1$ and $\sigma>2$. Let $L(t)$ be its ring-region similarity scale, $r_{\max}(t)$ its ring radius, and…