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A refined blow-up analysis of the Brezis-Nirenberg equation and its application: The one-bubble case for
Rui He, Xiangqing Liu, Juncheng Wei +1
In this paper, we consider the famous Brezis-Nirenberg equation \begin{eqnarray*} \left\{ \aligned &-Δu=λu+|u|^{\frac{4}{N-2}}u,\quad&\mbox{in}\,\, Ω,\\ &u=0,\quad&\mbox{on}\,\, \p…
On Brezis-Nirenberg problems: open questions and new results in dimension six
Fengliu Li, Giusi Vaira, Juncheng Wei +1
In this paper, we consider the Brezis-Nirenberg problem \begin{equation*} \left\{\begin{aligned} &-Δu = λu+|u|^{2^*-2}u, \quad &\mbox{in}\,Ω,\\ &u=0,\quad &\mbox{on}\, \partialΩ, \…
Construction of bubbling solutions of the Brezis-Nirenberg problem in general bounded domains (I): the dimensions 4 and 5
Fengliu Li, Giusi Vaira, Juncheng Wei +1
In this paper, we consider the Brezis-Nirenberg problem $$ -Δu=λu+|u|^{\frac{4}{N-2}}u,\quad\mbox{in}\,\, Ω,\quad u=0,\quad\mbox{on}\,\, \partialΩ, $$ where , $Ω\su…
Classification and Nondegeneracy of Cubic Nonlinear Schrödinger System in
Yujin Guo, Yong Luo, Juncheng Wei
We study the following one-dimensional cubic nonlinear Schrödinger system: \[ u_i''+2\Big(\sum_{k=1}^Nu_k^2\Big)u_i=-μ_iu_i \ \,\ \mbox{in}\, \ \mathbb{R} , \ \ i=1, 2, \cdots, N,…
Stability of the Caffarelli-Kohn-Nirenberg inequality along Felli-Schneider curve: critical points at infinity
Juncheng Wei, Yunze Wu
In this paper, we consider the following Caffarelli-Kohn-Nirenberg (CKN for short) inequality \begin{eqnarray*} \bigg(\int_{{\mathbb R}^d}|x|^{-b(p+1)}|u|^{p+1}dx\bigg)^{\frac{2}{p…
On some nonlinear Schrödinger equations in $\bbr^N$
Juncheng Wei, Yuanze Wu
In this paper, we introduce some new ideas to study Schrodinger equations in RN with power-type nonlinearities.
Stability of Caffarelli-Kohn-Nirenberg inequality
Juncheng Wei, Yuanze Wu
In this paper, we consider the Caffarelli-Kohn-Nirenberg (CKN) inequality: \begin{eqnarray*} \bigg(\int_{{\mathbb R}^N}|x|^{-b(p+1)}|u|^{p+1}dx\bigg)^{\frac{2}{p+1}}\leq C_{a,b,N}\…