3 problems

Assume $(B,T)$, $(u_{0},u_{1})$, $d$, and $\Omega$ are given, and let $u$ be the unique maximal solution to the hyperbolic problem. Critical-threshold conjecture. There exist criti…

Let $\Omega\subset\mathbb{R}^N$, with $1\leq N\leq 3$, be a bounded domain with smooth boundary, and let $u_0\in H^2\cap H_0^1(\Omega)$. Let $\lambda^{*}$ be the critical parameter…

Let $\Omega\subset\mathbb{R}^N$, with $1\leq N\leq 3$, be a bounded domain with smooth boundary, and let $u_0\in H^2\cap H_0^1(\Omega)$. Consider equation (1.1), its solution…