8 problems

For $1<p<N$, consider the critical quasi-linear Hénon equation … where $N\geq2$, $p_\alpha^*=\frac{p(N+\alpha)}{N-p}$, and $\alpha>0$. Gladiali–Grossi–Neves conjecture. Nonradial s…

Gladiali–Grossi–Neves conjecture. Non-radial positive solutions may exist only when $\alpha=\alpha_k$ for some $k\in\mathbb N$.

CFG08 extension conjecture. The proof of the analogous blow-up assertion can be carried out without assuming $u(0,t)=\max_{\Omega}u(\cdot,t)$, provided that the conclusions of Lemm…

Let $u_\alpha$ and $u_\beta$ be radial solutions of the Hénon problem … with the same number $n\geq1$ of nodal sets, where $B\subset\mathbb R^N$ is the unit open ball, $p>1$, and…

Conjecture A. Assume $\alpha>-2$ and

Fourth-order Hénon Liouville conjecture. If

Let $\alpha$ be the exponent in the Hénon equation considered in the paper, and let the nonradial solutions of Theorem 1.1 be the solutions obtained by bifurcation from the radial…

Let $N\geq 3$, let $\alpha>0$ and $p>1$, and consider the Neumann Hénon problem … A solution is positive, radial and increasing if it is positive, depends only on $|x|$, and is inc…