4 papers
Exact approximation order of real numbers in Cantor series expansions
Wanjin Cheng, Xinyun Zhang
Let be a sequence of integers with for all . For any real number , it can be expanded into the following infinite…
Hausdorff dimension of the Cartesian product of exact approximation set in -expansions
Wanjin Cheng, Xinyun Zhang
In this paper, we study the metrical theory of Cartesian products of exact approximation sets in -expansions. More precisely, for an integer and real numbers …
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…
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^…