4 problems

Let $\Phi_N^{(\beta)}(x,k)$ denote the radial functions, with matrix size $N$, parameter $\beta$, and variables $x$ and $k$ as in the recursive construction. Finite exponential-rat…

Let $N>k\geq 2$, $m\in\mathbb{N}$, and $p=\frac{N}{k}$. Let $R_{k,\gamma}$ denote the optimal constant in the critical Rellich inequality and let $R^{\rm rad}_{k,\gamma}$ denote it…

Assume $d\geqslant 2$, that the coefficient $a(t)$ or $A(s)$ is positive and locally Lipschitz continuous, and that $V(x)$ is a radial, locally bounded confining potential. Let…

Generalized Strauss restriction conjecture. The restriction $a<(n-1)q$ is not necessary for the generalized Strauss theorem to hold.