arXiv subjects

Yuanyang Yu

Publications and source records attributed to Yuanyang Yu.

7 recordsLinked to original sources

arXiv2025

Existence and multiplicity of $L^2$-Normalized solutions for the periodic Schr\"{o}dinger system of Hamiltonian type

In this paper, we study the following nonlinear Schr\"{o}dinger system of Hamiltonian type \begin{equation*} \left\{\begin{array}{l} -\Delta u+V(x)u=\partial_v H(x,u,v)+\omega v, \ x \in \mathbb{R}^N, \\ -\Delta v+V(x)v=\partial_u H(x,u,v)+\omega u,\ x \in \mathbb{R}^N, \\ \displaystyle\int_{\mathbb{R}^N}|z|^2dx=a^2, \end{array}\right. \end{equation*} where the potential function $V(x)$ is periodic, $z:=(u,v):\mathbb{R}^N\rightarrow \mathbb{R}\times\mathbb{R}$, $\omega\in \mathbb{R}$ appears as a Lagrange multiplier, $a>0$ is a prescribed constant. The existence and multiplicity of $L^2$-normalized solutions for the above Schr\"{o}dinger system are obtained, and the combination of the Lyapunov-Schmidt reduction, a perturbation argument and the multiplicity theorem of Ljusternik-Schnirelmann is involved in the proof. In addition, a bifurcation result is also given.

math.AP↗

arXiv2025

Critical fractional Kirchhoff problems: Uniqueness and Nondegeneracy

In this paper, we consider the following critical fractional Kirchhoff equation \begin{equation*} \Big(a+b{\int_{\mathbb{R}^{N}}}|(-\Delta)^{\frac{s}{2}}u|^2dx\Big)(-\Delta)^su=|u|^{2^*_s-2}u,\quad \text{in}\ \mathbb{R}^{N}, \end{equation*} where $a,b>0$, $\frac{N}{4}<s<1$, $2^*_s=\frac{2N}{N-2s}$ and $(-\Delta )^s$ is the fractional Laplacian. We prove the uniqueness and nondegeneracy of positive solutions to the problem, which can be used to study the singular perturbation problems concerning fractional Kirchhoff equations.

math.AP↗

arXiv2025

High-frequency magnetic response measurement of test mass with a fluxgate magnetometer for gravitational wave detection

For space-borne gravitational wave detectors,such as LISA and TianQin ,the disturbance caused by the coupling of test masses and the external magnetic fields is one of the main sources of the residual acceleration noise. Although the detection frequency band is from 0.1 mHz to 1 Hz, magnetic fields with frequencies higher than 1 Hz can still contribute to the noise through down conversion effect. Therefore, it is necessary to measure the AC magnetic susceptibility or magnetic response of the test mass at higher frequency for the evaluation of the magnetic noise. In this work, we propose a magnetic field response measurement method by directly probing the induced magnetic field of the test mass placed in a spatially uniform magnetic field. The frequency can be measured up to 1500 Hz, satisfying the requirement of space-borne gravitational wave detection.

physics.ins-det↗

arXiv2023

Existence and Multiplicity of Normalized Solutions for Dirac Equations with non-autonomous nonlinearities

In this paper, we study the following nonlinear Dirac equations \begin{align*} \begin{cases} -i\sum\limits_{k=1}^3\alpha_k\partial_k u+m\beta u=f(x,|u|)u+\omega u, \displaystyle \int_{\mathbb{R}^3} |u|^2dx=a^2, \end{cases} \end{align*} where $u: \mathbb{R}^{3}\rightarrow \mathbb{C}^{4}$, $m>0$ is the mass of the Dirac particle, $\omega\in \mathbb{R}$ arises as a Lagrange multiplier, $\partial_k=\frac{\partial}{\partial x_k}$, $\alpha_1,\alpha_2,\alpha_3$ are $4\times 4$ Pauli-Dirac matrices, $a>0$ is a prescribed constant, and $f(x,\cdot)$ has several physical interpretations that will be discussed in the Introduction. Under general assumptions on the nonlinearity $f$, we prove the existence of $L^2$-normalized solutions for the above nonlinear Dirac equations by using perturbation methods in combination with Lyapunov-Schmidt reduction. We also show the multiplicity of these normalized solutions thanks to the multiplicity theorem of Ljusternik-Schnirelmann. Moreover, we obtain bifurcation results of this problem.

math.AP↗

arXiv2023

Exploring the interfacial coupling between graphene and the antiferromagnetic insulator MnPSe$_3$

Interfacial coupling between graphene and other 2D materials can give rise to intriguing physical phenomena. In particular, several theoretical studies predict that the interplay between graphene and an antiferromagnetic insulator could lead to the emergence of quantum anomalous Hall phases. However, such phases have not been observed experimentally yet, and further experimental studies are needed to reveal the interaction between graphene and antiferromagnetic insulators. Here, we report the study in heterostructures composed of graphene and the antiferromagnetic insulator MnPSe$_3$. It is found that the MnPSe$_3$ has little impact on the quantum Hall phases apart from doping graphene via interfacial charge transfer. However, the magnetic order can contribute indirectly via process like Kondo effect, as evidenced by the observed minimum in the temperature-resistance curve between 20-40 K, far below the N\'eel temperature (70 K).

cond-mat.mtrl-sci↗

arXiv2020

Existence and concentration of solution for Schr\"odinger-Poisson system with local potential

In this paper, we study the following nonlinear Schr\"odinger-Poisson type equation \begin{equation*} \begin{cases} -\varepsilon^2\Delta u+V(x)u+K(x)\phi u=f(u)&\text{in}\ \mathbb{R}^3,\\ -\varepsilon^2\Delta \phi=K(x)u^2&\text{in}\ \mathbb{R}^3, \end{cases} \end{equation*} where $\varepsilon>0$ is a small parameter, $V: \mathbb{R}^3\rightarrow \mathbb{R}$ is a continuous potential and $K: \mathbb{R}^3\rightarrow \mathbb{R}$ is used to describe the electron charge. Under suitable assumptions on $V(x), K(x)$ and $f$, we prove existence and concentration properties of ground state solutions for $\varepsilon>0$ small. Moreover, we summarize some open problems for the Schr\"odinger-Poisson system.

math.AP↗

arXiv2020

An infinite sequence of localized nodal solutions for Schr\"odinger-Poisson system with double potentials

In this paper, we study the existence of localized sign-changing (or nodal) solutions for the following nonlinear Schr\"odinger-Poisson system \begin{equation*} \begin{cases} -\varepsilon^2 \Delta u+V(x)u+\phi u=K(x)f(u),&\text{in}~\mathbb{R}^3,\\ -\varepsilon^2 \Delta \phi=u^2,&\text{in}~ \mathbb{R}^3, \end{cases} \end{equation*} where $\varepsilon>0$ is small parameters, the linear potential $V$ and nonlinear potential $K$ are bounded and bounded away from zero. By using the penalization method together with the method of invariant sets of descending flow, we establish the existence of an infinite sequence of localized sign-changing solutions which are higher topological type solutions given by the minimax characterization of the symmetric mountain pass theorem and we determine a concrete set as the concentration position of these sign-changing solutions. For single potential, that is, linear potential $V$ or nonlinear potential $K$ is a positive constant, we prove that these localized sign-changing solutions concentrated near a local minimum set of the potential $V$ or a local maximum set of the potential $K$. Moreover, our method is works for the following nonlinear Schr\"odinger equation \begin{equation*} -\varepsilon^2 \Delta u+V(x)u=K(x)f(u),~\text{in}~\mathbb{R}^N \end{equation*} where $N\geq 2$. The result generalizes the result by Chen and Wang (Calc.Var.Partial Differential Equations 56:1-26, 2017).

math.AP↗