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math.AP2022
The helical vortex filaments of Ginzburg-Landau system in
Lipeng Duan, Qi Gao, Jun Yang
We consider the following coupled Ginzburg-Landau system in \begin{align*} \begin{cases} -ε^2 Δw^+ +\Big[A_+\big(|w^+|^2-{t^+}^2\big)+B\big(|w^-|^2-{t^-}^2\big)\Big…
math.AP2022
Doubling the equatorial for the prescribed scalar curvature problem on
Lipeng Duan, Monica Musso, Suting Wei
We consider the prescribed scalar curvature problem on $$ Δ_{{\mathbb S}^N} v-\frac{N(N-2)}{2} v+\tilde{K}(y) v^{\frac{N+2}{N-2}}=0 \quad \mbox{on} \ {\mathbb S}…
math.AP2022
Positive solutions for a critical elliptic equation
Lipeng Duan, Shuying Tian
In this paper, we are concerned with the following elliptic equation \begin{equation*} \begin{cases} -Δu= Q(x)u^{2^*-1 }+\varepsilon u^{s},~ &{\text{in}~Ω},\\[1mm] u>0,~ &{\text{in…