From the 2 of 5 linked papers with an AI index.
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Sharp Quantitative Stability for the Affine \(p\)-Sobolev Inequality, Part I: The Case \(2\le p<n\)
Song Fan, Gui-Dong Li, Jianjun Zhang
The authors establish a sharp quantitative stability theorem for the affine L^p‑Sobolev inequality in the range 2 ≤ p < n, proving that the stability exponent is exactly p and cann…
Sharp Stability for the Affine Fractional Sobolev Inequality
Song Fan, Gui-Dong Li, Jianjun Zhang
The paper proves a precise quantitative stability result for an affine fractional Sobolev inequality, identifying key spectral properties and showing the optimal global stability c…
Stability of the Sobolev--Escobar bridge inequality
Fan Song, Li Gui-Dong, Zhang Jianjun
We study the local stability of the bridge family \[ Φ(T):=\inf_{u\in\mathcal A_T}\|\nabla u\|_{L^2(\mathbb R^n_+)}, \qquad T>0,\quad n\ge3, \] where \[ \mathcal A_T := \Bigl\{ u\…
On the existence of normalized solutions to a class of fractional Choquard equation with potentials
Yongpeng Chen, Zhipeng Yang, Jianjun Zhang
This paper investigates the existence of normalized solutions to the nonlinear fractional Choquard equation: $$ (-Î)^s u+V(x) u=λu+f(x)\left(I_α*\left(f|u|^q\right)\right)|u|^{q…
On the existence of multiple normalized solutions for a class of fractional Choquard equations with mixed nonlinearities
Yongpeng Chen, Zhipeng Yang, Jianjun Zhang
We investigate the existence of normalized solutions for the following nonlinear fractional Choquard equation: $$ (-Î)^s u+V(εx)u=λu+\left(I_α*|u|^q\right)|u|^{q-2} u+\left(I_Î…