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math.AP2026
Sharp Quantitative Stability for the Affine \(p\)-Sobolev Inequality, Part I: The Case \(2\le p<n\)
Song Fan, Gui-Dong Li, Jianjun Zhang
We prove a sharp quantitative stability result for the affine \(L^p\)-Sobolev inequality, for \(p\ge2\), introduced by Lutwak--Yang--Zhang (\emph{J. Differential Geom.}, \textbf{62…
math.AP2025
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: $$ (-Δ)^s u+V(x) u=λu+f(x)\left(I_α*\left(f|u|^q\right)\right)|u|^{q-2}…
math.AP2024
On the existence of multiple normalized solutions for a class of fractional Choquard equations with mixed nonlinearities
Yongpeng Chen, Zhipeng Yang, Jianjun Zhang
We investigate the existence of normalized solutions for the following nonlinear fractional Choquard equation: $$ (-Δ)^s u+V(εx)u=λu+\left(I_α*|u|^q\right)|u|^{q-2} u+\left(I_α*|u|…