3 papers
math.NT2024
Hausdorff dimension of some exceptional sets in Lüroth expansions
Ao Wang, Xinyun Zhang
In this paper, we study the metrical theory of the growth rate of digits in Lüroth expansions. More precisely, for , let $ \left[ d_1\left( x \right) ,d_…
math.AP2024
Existence of infinitely many solutions for a critical Hartree type equation with potential: local Pohožaev identities methods
Daniele Cassani, Minbo Yang, Xinyun Zhang
This paper deals with the following equation $$-Δu =K(|x'|, x'')\Big(|x|^{-α}\ast (K(|x'|, x'')|u|^{2^{\ast}_α})\Big) |u|^{2^{\ast}_α-2}u\quad\mbox{in}\ \mathbb{R}^N,$$ where $N\ge…
math.AP2023
Nondegeneracy of positive solutions for a biharmonic hartree equation and its applications
Xinyun Zhang, Weiwei Ye, Minbo Yang
In this paper, we are interested in some problems related to the following biharmonic hartree equation \begin{equation*} Δ^{2} u=(|x|^{-α}\ast |u|^{p})u^{p-1},\sp \text{in}\quad\R^…