11 citations · 29 across the 12 of their papers we have counts for
11 papers · 1 filter
Signs of high order derivatives for the theta and Epstein zeta functions and application
Deng Kaixin, Luo Senping
In the 1950s, 1960s and 1988, number theorists Rankin \cite{Ran1953}, Cassels \cite{Cas1959}, Ennola \cite{Enn1964a}, Diananda \cite{Dia1964}, and Montgomery \cite{Mon1988} derived…
A new type of minimizers in lattice energy and its application
Kaixin Deng, Senping Luo
Let and $\mathcal{K}(α;z):=\sum_{ (m,n)\in \mathbb{Z} ^2 }\frac{{\left| mz+n \right|}^2}{{{\Im}(z)}}e^{-πα\frac{ \left|mz+n\right…
Minimizing Lattice Energy and Hexagonal Crystallization
Kaixin Deng, Senping Luo
Consider the energy per particle on the lattice given by , where and is a tw…
On a variational model for the continuous mechanics exhibiting hexagonal to square Phase Transitions
Senping Luo, Juncheng Wei
Inspired by Conti and Zanzotto \cite{Conti2004A}, we reformulate a simple variational model for reconstructive phase transitions in crystals arising in continuum mechanics in the f…
On lattice hexagonal crystallization for non-monotone potentials
Senping Luo, Juncheng Wei
Let where be the two dimensional lattices…
On Minima of Difference of Epstein Zeta Functions and Exact Solutions to Lennard-Jones Lattice Energy
Senping Luo, Juncheng Wei
Let be the Eisenstein series/Epstein Zeta function. Motivated by widely used Lennard-Jones potenti…
On minima of sum of theta functions and Mueller-Ho Conjecture
Senping Luo, Juncheng Wei
Let and be the theta function associated with the lattic…
On finite Morse index solutions to the quadharmonic Lane-Emden equation
Senping Luo, Juncheng Wei, Wenming Zou
In this paper, we compute the Joseph-Lundgren exponent for the quadharmonic Lane-Emden equation, derive a monotonicity formula and classify the finite Morse index solution to the f…
Classification of the stable solution to the fractional Lane-Emden equation
Senping Luo, Juncheng Wei, Wenming Zou
We classify the stable solutions (positive or sign-changing, radial or not) to the following nonlocal Lane-Emden equation: in for .
Existence, nonexistence, symmetry and uniqueness of ground state for critical Schrödinger system involving Hardy term
Senping Luo, Wenming Zou
We study the following elliptic system with critical exponent: \begin{displaymath} \begin{cases}-Δu_j-\frac{λ_j}{|x|^2}u_j=u_j^{2^*-1}+\sum\limits_{k\neq j}β_{jk}α_{jk}u_j^{α_{jk}-…
On the triharmonic Lane-Emden equation
Senping Luo, Juncheng Wei, Wenming Zou
We derive a monotonicity formula and classify finite Morse index solutions (positive or sign-changing, radial or not) to the following triharmonic Lane-Emden equation: \begin{equat…