4 papers · 1 filter
Sharp Born--Infeld Sobolev inequality and extremal functions on the lattice graph
Chao Ji, Kai Sheng
In this paper, we study the sharp Sobolev-type inequality associated with the Born--Infeld energy on the lattice graph \(\mathbb Z^N\), \(N\geq3\): \[ \frac12\sum_{x\in\mathbb Z^N}…
Normalized solutions of -supercritical NLS equations with periodic potentials
Zhentao He, Norihisa Ikoma, Chao Ji
In this paper, we study normalized solutions to the following -supercritical nonlinear Schrödinger equation with a periodic potential \begin{equation*} \begin{dcases} -Δu +V (…
A partial answer to Brezis' Open Problem 2.1
Chao Ji, Kai Sheng
In this paper, we give a partial answer to Brezis' Open Problem~2.1, which concerns the uniqueness of solutions to the Ginzburg--Landau equation in the unit disc with the degree-on…
Singular limit of lattice graphs and its application to critical Lane--Emden equations on lattice graphs
Zhentao He, Chao Ji
In this paper, we establish new connections between lattice graphs and metric grids, providing a unified framework for the study of singular limit problems and Gagliardo--Nirenberg…