2 problems

For $s\in\mathbb{N}$, let $m\in\mathbb{N}$ and define the boundary Poisson kernels … for $k\in\{0,\ldots,m\}$, $y\in\partial\mathbb{R}^N_+$, and $x\in\mathbb{R}^N\setminus\{y\}$. U…

Let $\mathcal{H}=I-\Delta-p\left\lvert\phi\right\rvert^{p-1}\psi$ be the linearization associated with the Dirichlet problem, and compare its unstable eigenvalues with those of the…