5 papers · 1 filter
The fractional Hénon-Lane-Emden conjecture and some critical nonexistence phenomena
Kui Li, Haoyang Lu, Zhitao Zhang
We refine the proof method for the Hénon-Lane-Emden system and extend it to fractional orders , proving subcritical nonexistence of positive classical solutions. And we find…
On a new region for the Lane-Emden conjecture in higher dimensions
Kui Li, Mingxiang Li, Juncheng Wei
We study the Lane-Emden conjecture, which asserts the non-existence of non-trivial, non-negative solutions to the Lane-Emden system \[ -Δu = v^p, \quad -Δv = u^q, \quad x \in \math…
Symmetry and classification of positive solutions of some weighted elliptic equations
Kui Li, Mengyao Liu, Jianfeng Wu
We study the weighted elliptic equation \begin{equation} -div(|x|^{-2a}\nabla u)=|x|^{-bp}|u|^{p-2}u~~~\mbox{in}~\mathbb{R}^N ~~~~~~~~~~~~~~~~~~~~(0.1)\end{equation} with …
Classification of stationary solutions of the -dimensional radial Yang-Mills equation
Kui Li, Zhitao Zhang
We classify the solutions of the planar weighted Allen-Cahn equation arising from the critical equivariant Yang-Mills problem. We first give a complete classification for r…
On the Lane-Emden conjecture
Kui Li, Zhitao Zhang
We consider the Lane-Emden conjecture which states that there is no non-trivial non-negative solution for the Lane-Emden system whenever the pair of exponents is subcritical. By So…