Qiao Hua

Critical GJMS Equations on $\mathbb{H}^n \times \mathbb{S}^m$

Let $M=\mathbb{H}^n\times\mathbb{S}^m$, where $n\geq 2$, $m\geq 1$, and $N=n+m$. Let $P_k$ be the order-$2k$ GJMS operator, with $1\leq k<N/2$, and assume that $\Lambda_0=\inf\sigma_{L^2(M)}(P_k)>0$. We study$$P_kU-\lambda U=|U|^{q-2}U,\qquad q=\frac{2N}{N-2k},\qquad 0<\lambda\leq\Lambda_0,$$and attainment of the assoc...