3 papers
math.AP2025
The Li-Lin's open problem on
Zhi-Yun Tang, Xianhua Tang
In 2012, Y.Y. Li and C.-S. Lin (Arch. Ration. Mech. Anal., 203(3): 943-968) posed an open problem concerning the existence of positive solutions to the elliptic equation $$ \begin{…
math.AP2025
A positive solution of the elliptic equation on a starshaped domain with boundary singularities
Zhi-Yun Tang, Xianhua Tang
We consider the elliptic equation with boundary singularities \begin{equation} \begin{cases} -Δu=-λ|x|^{-s_{1}}|u|^{p-2}u+|x|^{-s_{2}}|u|^{q-2}u &\text { in } \varOmega , u(x)=0 &\…
math.AP2024
On Li-Lin's open problem
Zhi-Yun Tang, Xianhua Tang
In this paper, we give a first negative answer to a question proposed by Li and Lin (Arch Ration Mech Anal 203(3): 943-968, 2012). Meanwhile we also give a second positive answer t…