arXiv subjects

Zhi-Qiang Wang

Publications and source records attributed to Zhi-Qiang Wang.

16 recordsLinked to original sources

arXiv2026

Nonlinear Schrödinger systems with all attractive forces

In this paper we investigate in a systematic way the solution structure of nonnegative solutions for coupled nonlinear Schrödinger systems in the all attractive regime. For all frequencies equal case we obtain results on Morse index of synchronized positive vector solutions and nonnegative semi-vector solutions as well as their kernel of linearized systems at these solutions. We establish a variational characterization of synchronized positive vector solutions and as applications we give a new existence result about positive vector solutions for the general systems with arbitrary frequencies. We also examine the synchronization phenomenon of positive vector solutions, and prove that if the interaction matrix has exactly one positive eigenvalue, any positive vector solution is synchronized. Finally we provide examples of domains for which synchronization of positive solutions fails to hold if the interaction matrix has at least two positive eigenvalues. Our results reveal the effect of the spectral information of the interaction matrix of the couplings and geometry of a domain on the solution structure.

math.AP↗

arXiv2025

Multiple existence and qualitative property of nodal solutions for coupled elliptic equations

The paper studies nodal solutions having prescribed componentwise nodal data for the following coupled nonlinear elliptic equations \begin{equation} \left\{ \begin{array}{lr} -Δu_{j}+ u_{j}= u^{3}_{j}+β\sum_{i=1, i\neq j}^N u_{j}u_{i}^{2} \,\,\,\,\,\,\, \mbox{in}\ Ω,\nonumber u_{j}\in H_{0,r}^{1}(Ω), \,\,\,\,\,\,\,\,j=1,\dots,N.\nonumber \end{array} \right. \end{equation} Here, $Ω\subset\mathbb{R}^n$ is a bounded and radial domain with $n=2,3$. The coupling constant $β\leq-1$ is in the repulsive regime. We investigate the solution structure for both positive and nodal solutions, proving multiple existence of solutions with prescribed nodal data and providing qualitative estimates for the nodal numbers of the inter-componentwise differences of solutions with both upper and lower bounds. Our general framework is for nodal solutions though our results are new also for positive solutions.

math.AP↗

arXiv2025

Global bifurcations of nodal solutions for coupled elliptic equations

We investigate the global bifurcation structure of the radial nodal solutions to the coupled elliptic equations \begin{equation} \left\{ \begin{array}{lr} -Δu+u=u^3+βuv^2\mbox{ in }B_1 ,\nonumber -Δv+v=v^3+βu^2v\mbox{ in }B_1 ,\nonumber u,v\in H_{0,r}^1(B_1).\nonumber \end{array} \right. \end{equation} Here $B_1$ is a unit ball in $\mathbb{R}^3$ and $β\in\mathbb{R}$ the coupling constant is used as bifurcation parameter. For each $k$, the unique pair of nodal solutions $\pm w_k$ with exactly $k-1$ zeroes to the scalar field equation $-Δw + w=w^3$ generate exactly four synchronized solution curves and exactly four semi-trivial solution curves to the above system. We obtain a fairly complete global bifurcation structure of all bifurcating branches emanating from these eight solution curves of the system, and show that for different $k$ these bifurcation structures are disjoint. We obtain exact and distinct nodal information for each of the bifurcating branches, thus providing a fairly complete characterization of nodal solutions of the system in terms of the coupling.

math.AP↗

arXiv2023

Multiple Non-radial Solutions for Coupled Schrödinger Equations

The paper deals with the existence of non-radial solutions for an $N$-coupled nonlinear elliptic system. In the repulsive regime with some structure conditions on the coupling and for each symmetric subspace of rotation symmetry, we prove the existence of an infinite sequence of non-radial positive solutions and an infinite sequence of non-radial nodal solutions.

math.AP↗

arXiv2023

Astrometric Reduction of Saturnian Satellites with Cassini-ISS Images Degraded by Trailed Stars

Imaging Science Subsystem (ISS) mounted on the Cassini spacecraft has taken a lot of images, which provides an important source of high-precision astrometry of some planets and satellites. However, some of these images are degraded by trailed stars. Previously, these degraded images cannot be used for astrometry. In this paper, a new method is proposed to detect and compute the centers of these trailed stars automatically. The method is then performed on the astrometry of ISS images with trailed stars. Finally, we provided 658 astrometric positions between 2004 and 2017 of several satellites that include Enceladus, Dione, Tethys, Mimas and Rhea. Compared with the JPL ephemeris SAT427, the mean residuals of these measurements are 0.11 km and 0.26 km in right ascension and declination, respectively. Their standard deviations are 1.08 km and 1.37 km, respectively. The results show that the proposed method performs astrometric measurements of Cassini ISS images with trailed stars effectively.

astro-ph.EP↗

arXiv2020

Analysis of open source license selection for the GitHub programming community

Developers usually select different open source licenses to restrain the conditions of using open source software, in order to protect intellectual property rights effectively and maintain the long-term development of the software. However, the open source community has a wide variety of licenses available, developers generally find it difficult to understand the differences between different open source license. And existing open source license selection tools require developers to understand the terms of the open source license and identify their business needs, which makes it hard for developers to make the right choice. Although academia has extensive research to the open source license, but there is no systematic analysis on the actual difficulties of the developers to choose the open source license, thus lacking a clear understanding, for this reason, the purpose of this paper is to understand the difficulties faced by open source developers in choosing open source licenses, analyze the components of open source license and the affecting factors of open source license selection, and to provide references for developers to choose open source licenses.

cs.SE↗

arXiv2020

Multiple nodal solutions having shared componentwise nodal numbers for coupled Schrödinger equations

We investigate the structure of nodal solutions for coupled nonlinear Schrödinger equations in the repulsive coupling regime. Among other results, for the following coupled system of $N$ equations, we prove the existence of infinitely many nodal solutions which share the same componentwise-prescribed nodal numbers \begin{equation}\label{ab} \left\{ \begin{array}{lr} -Δu_{j}+λu_{j}=μu^{3}_{j}+\sum_{i\neq j}βu_{j}u_{i}^{2} \,\,\,\,\,\,\, in\ \W , u_{j}\in H_{0,r}^{1}(\W), \,\,\,\,\,\,\,\,j=1,\dots,N, \end{array} \right. \end{equation} where $\W$ is a radial domain in $\mathbb R^n$ for $n\leq 3$, $λ>0$, $μ>0$, and $β<0$. More precisely, let $p$ be a prime factor of $N$ and write $N=pB$. Suppose $β\leq-\fracμ{p-1}$. Then for any given non-negative integers $P_{1},P_{2},\dots,P_{B}$, (\ref{ab}) has infinitely many solutions $(u_{1},\dots,u_{N})$ such that each of these solutions satisfies the same property: for $b=1,...,B$, $u_{pb-p+i}$ changes sign precisely $P_b$ times for $i=1,...,p$. The result reveals the complex nature of the solution structure in the repulsive coupling regime due to componentwise segregation of solutions. Our method is to combine a heat flow approach as deformation with a minimax construction of the symmetric mountain pass theorem using a $\mathbb Z_p$ group action index. Our method is robust, also allowing to give the existence of one solution without assuming any symmetry of the coupling.

math.AP↗

arXiv2019

A quasilinear Schrödinger equation with Hartree type nonlinearity

In this paper, we deal with the Cauchy problem of the quasilinear Schödinger equation \begin{equation*} \left\{ \begin{array}{lll} iu_t=Δu+2uh'(|u|^2)Δh(|u|^2)+(W(x)\ast|u|^2)u,\ x\in \mathbb{R}^N,\ t>0\\ u(x,0)=u_0(x),\quad x\in \mathbb{R}^N. \end{array}\right. \end{equation*} Here $h(s)$ and $W(x)$ are some real valued functions. Our focus is to investigate how the interplay between the potential $W(x)$ and the quasilinear presence $h(s)$ affects the blowup in finite time and global existence of the solution. In a special, we can obtain the watershed condition on $W(x)$ in the following sense: If $W(x)\in L^1(\mathbb{R}^N)\cap \{L^q(\mathbb{R}^N)+L^{\infty}(\mathbb{R}^N)\} $, then exist $q_c$ and $q_s$ such that the solution is global existence for any initial data in the energy space when $q>q_c$ and the solution maybe blow up in finite time for some initial data when $q_s<q<q_c$, and for $q=q_c$ whether the solution is global existence or not depend on the initial data.

math.AP↗

arXiv2019

Review of borophene and its potential applications

Since two-dimensional boron sheet (borophene) synthesized on Ag substrates in 2015, research on borophene has grown fast in the fields of condensed matter physics, chemistry, material science, and nanotechnology. Due to the unique physical and chemical properties, borophene has various potential applications. In this review, we summarize the progress on borophene with a particular emphasis on the recent advances. First, we introduce the phases of borophene by experimental synthesis and theoretical predictions. Then, the physical and chemical properties, such as mechanical, thermal, electronic, optical and superconducting properties are summarized. We also discuss in detail the utilization of the borophene for wide ranges of potential application among the alkali metal ion batteries, Li-S batteries, hydrogen storage, supercapacitor, sensor and catalytic in hydrogen evolution, oxygen reduction, oxygen evolution, and CO2 electroreduction reaction. Finally, the challenges and outlooks in this promising field are featured on the basis of its current development.

cond-mat.mtrl-sci↗

arXiv2018

Limit Behavior of Mass Critical Hartree Minimization Problems with Steep Potential Wells

We consider minimizers of the following mass critical Hartree minimization problem: \[ e_λ(N):=\underset{\{u\in H^1(R^d),\,\|u\|^2_2=N\}}{\inf} E_λ(u),\,\ d\ge 3, \] where the Hartree energy functional $E_λ(u)$ is defined by \[ E_λ(u):=\int_{R ^d}|\nabla u(x)|^2dx+λ\int_{R ^d}g(x)u^2(x)dx-\frac{1}{2} \int_{R ^d}\int_{R ^d} \frac{u^2(x)u^2(y)}{|x-y|^2}dxdy,\,\ λ>0,\] and the steep potential $g(x)$ satisfies $0=g(0)=\inf _{R^d}g(x)\le g(x)\le 1$ and $1-g(x)\in L^{\frac{d}{2}}(R^d)$. We prove that there exists a constant $N^*>0$, independent of $λg(x)$, such that if $N\ge N^*$, then $e_λ(N)$ does not admit minimizers for any $λ>0$; if $0 0$ such that $e_λ(N)$ admits minimizers for any $λ>λ^*(N)$, and $e_λ(N)$ does not admit minimizers for $0<λ<λ^*(N)$. For any given $0<N<N^*$, the limit behavior of positive minimizers for $e_λ(N)$ is also studied as $λ\to\infty$, where the mass concentrates at the bottom of $g(x)$.

math.FA↗

arXiv2017

New crystal structure prediction of fully hydrogenated borophene by first principles calculations

New crystal structures of fully hydrogenated borophene (borophane) have been predicted by first principles calculation. Comparing with the chair-like borophane (C-boropane) that has been reported in literature, we obtained four new borophane conformers with much lower total-energy. The most stable one, washboard-like borophane (W-borophane), has energy about 113.41 meV/atom lower than C-borophane. In order to explain the relative stability of different borophane conformers, the atom configuration, density of states, charge transfer, charge density distribution and defect formation energy of B-H dimer have been calculated. The results show that the charge transfer from B atoms to H atoms is crucial for the stability of borophane. In different borophane conformers, the bonding characteristics between B and H atoms are similar, but the B-B bonds in W-borophane are much stronger than that in C-borophane or other structures. In addition, we examined the dynamical stability of borophane conformers by phonon dispersions and found that the four new conformers are all dynamically stable. Finally the mechanical properties of borophane conformers along an arbitrary direction have been discussed. W-borophane possesses unique electronic structure (Dirac cone), good stability and superior mechanical properties. W-borophane has broad perspective for nano electronic device.

cond-mat.mtrl-sci↗

arXiv2016

Local and Global Dynamic Bifurcations of Nonlinear Evolution Equations

We present new local and global dynamic bifurcation results for nonlinear evolution equations of the form $u_t+A u=f_λ(u)$ on a Banach space $X$, where $A$ is a sectorial operator, and $λ\in R$ is the bifurcation parameter. Suppose the equation has a trivial solution branch $\{(0,λ):\,\,λ\in R\}$. Denote $Φ_λ$ the local semiflow generated by the initial value problem of the equation. It is shown that if the crossing number $n$ at a bifurcation value $λ=λ_0$ is nonzero and moreover, $S_0=\{0\}$ is an isolated invariant set of $Φ_{λ_0}$, then either there is a one-sided neighborhood $I_1$ of $λ_0$ such that $Φ_λ$ bifurcates a topological sphere $\mathbb{S}^{n-1}$ for each $λ\in I_1\setminus\{λ_0\}$, or there is a two-sided neighborhood $I_2$ of $λ_0$ such that the system $Φ_λ$ bifurcates from the trivial solution an isolated nonempty compact invariant set $K_λ$ with $0\not\in K_λ$ for each $λ\in I_2\setminus\{λ_0\}$. We also prove that the bifurcating invariant set has nontrivial Conley index. Building upon this fact we establish a global dynamical bifurcation theorem. Roughly speaking, we prove that for any given neighborhood $Ω$ of the bifurcation point $(0,λ_0)$, the connected bifurcation branch $Γ$ from $(0,λ_0)$ either meets the boundary $\partialΩ$ of $Ω$, or meets another bifurcation point $(0,λ_1)$. This result extends the well-known Rabinowitz's Global Bifurcation Theorem to the setting of dynamic bifurcations of evolution equations without requiring the crossing number to be odd. As an illustration example, we consider the well-known Cahn-Hilliard equation. Some global features on dynamical bifurcations of the equation are discussed.

math.DS↗

arXiv2015

Multiple normalized solutions for quasi-linear Schrödinger equations

In this paper we prove the existence of two solutions having a prescribed $L^2$-norm for a quasi-linear Schrödinger equation. One of these solutions is a mountain pass solution relative to a constraint and the other one a minimum either local or global. To overcome the lack of differentiability of the associated functional, we rely on a perturbation method developed in [27].

math.AP↗

arXiv2015

Properties of ground states of attractive Gross-Pitaevskii equations with multi-well potentials

We are interested in the attractive Gross-Pitaevskii (GP) equation in $\R^2$, where the external potential $V(x)$ vanishes on $m$ disjoint bounded domains $Ω_i\subset \R^2\ (i=1,2,\cdots,m)$ and $V(x)\to\infty$ as $|x|\to\infty$, that is, the union of these $Ω_i$ is the bottom of the potential well. By making some delicate estimates on the energy functional of the GP equation, we prove that when the interaction strength $a$ approaches some critical value $a^*$ the ground states concentrate and blow up at the center of the incircle of some $Ω_j$ which has the largest inradius. Moreover, under some further conditions on $V(x)$ we show that the ground states of GP equations are unique and radially symmetric at leat for almost every $a \in (0, a^*)$.

math.AP↗

arXiv2014

Infinitely many sign-changing solutions for the nonlinear Schrödinger-Poisson system

We investigate the existence of multiple bound state solutions, in particular sign-changing solutions. By using the method of invariant sets of descending flow, we prove that this system has infinitely many sign-changing solutions. In particular, the nonlinear term includes the power-type nonlinearity $f(u)=|u|^{p-2}u$ for the well-studied case $p\in(4,6)$, and the less-studied case $p\in(3,4)$, and for the latter case few existence results are available in the literature.

math.AP↗

arXiv2014

Bifurcations for a Coupled Schrödinger System with Multiple Components

In this paper, we study local bifurcations of an indefinite elliptic system with multiple components: \begin{equation*} \left\{\begin{array}{ll} -Δu_j + au_j = μ_ju_j^3+β\sum_{k\ne j}u_k^2u_j, u_j>0\ \ \hbox{in}\ Ω, u_j=0 \ \ \hbox{on}\ \partialΩ,\ j=1,\dots,n. \end{array} \right. \end{equation*} Here $Ω\subset{\mathbb{R}}^N$ is a smooth and bounded domain, $n\ge3$, $a<-Λ_1$ where $Λ_1$ is the principal eigenvalue of $(-Δ, H_0^1(Ω))$; $μ_j$ and $β$ are real constants. Using the positive and non-degenerate solution of the scalar equation $-Δω-ω=-ω^3$, $ω\in H_0^1(Ω)$, we construct a synchronized solution branch $\mathcal{T}_ω$. Then we find a sequence of local bifurcations with respect to $\mathcal{T}_ω$, and we find global bifurcation branches of partially synchronized solutions.

math.AP↗