8 problems

For $d>2$, consider nonnegative, nontrivial subsolutions of the Lane–Emden inequality … and let $M_c^{sub}(d)$ be the corresponding minimal mass. Let $M_c(d)$ denote the Keller–Seg…

Let $M_c^{sub}(d)$ denote the minimal mass of nonnegative, nontrivial subsolutions of the Lane–Emden equation … and let $M_c(d)$ be the critical mass of the Keller–Segel system. Cr…

Fractional Lane–Emden conjecture. If

Let $u_p$ be a family of positive solutions satisfying the energy limit … Assume that the solutions concentrate at $k$ points, with concentration masses $m_1,\ldots,m_k$, and let…

Negative-bubble conjectures. Motivated by the radial case, one should have

Positive-bubble height conjecture. Motivated by the radial case, one should have

Supremum-limit conjecture. The limit of the supremum norm should be

Let $1<p<N-1$, let $q_c$ be the critical exponent defined in the paper, and let $S\subset S^{N-1}_+$ be star-shaped. Consider the boundary-value problem … is that this problem admi…