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Quite differently from those perturbation techniques in \cite{DM}, we use the assumption of a $C^1$-stable critical point to construct positive or sign-changing bubbling solutions to the boundary value problem $-\Delta u=\lambda u|u|^{p-2}e^{|u|^p}$ with homogeneous Dirichlet boundary condition in a bounded, smooth planar domain $\Omega$, when $00$ is a small parameter. A sufficient condition on the intersection between the nodal line of these sign-changing solutions and the boundary of the domain is founded. Moreover, for $\lambda$ small enough, we prove that when $\Omega$ is an arbitrary bounded domain, this problem has not only at least two pairs of bubbling solutions which change sign exactly once and whose nodal lines intersect the boundary, but also a bubbling solution which changes sign exactly twice or three times; when $\Omega$ has an axial symmetry, this problem has a bubbling solution which alternately changes sign arbitrarily many times along the axis of symmetry through the domain.

In this paper, we investigate the quasi-neutral limit of Nernst-Planck-Navier-Stokes system in a smooth bounded domain $\Omega$ of $\mathbb{R}^d$ for $d=2,3,$ with ``electroneutral boundary conditions" and well-prepared data. We first prove by using modulated energy estimate that the solution sequence converges to the limit system in the norm of $L^\infty((0,T);L^2(\Omega))$ for some positive time $T.$ In order to justify the limit in a stronger norm, we need to construct both the initial layers and weak boundary layers in the approximate solutions.

Given a bounded smooth domain $\Omega$ in $\mathbb{R}^2$, we study the following anisotropic elliptic problem $$ \begin{cases} -\nabla\big(a(x)\nabla \upsilon\big)= a(x)\big[e^{\upsilon}-s\phi_1-4\pi\alpha\delta_q-h(x)\big]\,\,\,\, \,\textrm{in}\,\,\,\,\,\Omega,\\[2mm] \upsilon=0 \qquad\qquad\qquad\qquad\qquad \qquad\qquad\qquad\qquad\quad \textrm{on}\,\ \,\partial\Omega, \end{cases} $$ where $a(x)$ is a positive smooth function, $s>0$ is a large parameter, $h\in C^{0,\gamma}(\overline{\Omega})$, $q\in\Omega$, $\alpha\in(-1,+\infty)\setminus\mathbb{N}$, $\delta_q$ denotes the Dirac measure with pole at point $q$ and $\phi_1$ is a positive first eigenfunction of the problem $-\nabla\big(a(x)\nabla \phi\big)=\lambda a(x)\phi$ under Dirichlet boundary condition in $\Omega$. We show that if $q$ is both a local maximum point of $\phi_1$ and an isolated local maximum point of $a(x)\phi_1$, this problem has a family of solutions $\upsilon_s$ with arbitrary $m$ bubbles accumulating to $q$ and the quantity $\int_{\Omega}a(x)e^{\upsilon_s}\rightarrow8\pi(m+1+\alpha)a(q)\phi_1(q)$ as $s\rightarrow+\infty$, which give a positive answer to the Lazer-McKenna conjecture for this case., Comment: arXiv admin note: text overlap with arXiv:1908.05532

The potential advantages of intelligent wireless communications with millimeter wave (mmWave) and massive multiple-input multiple-output (MIMO) are based on the availability of instantaneous channel state information (CSI) at the base station (BS). However, no existence of channel reciprocity leads to the difficult acquisition of accurate CSI at the BS in frequency division duplex (FDD) systems. Many researchers explored effective architectures based on deep learning (DL) to solve this problem and proved the success of DL-based solutions. However, existing schemes focused on the acquisition of complete CSI while ignoring the beamforming and precoding operations. In this paper, we propose an intelligent channel feedback architecture using eigenmatrix and eigenvector feedback neural network (EMEVNet). With the help of the attention mechanism, the proposed EMEVNet can be considered as a dual channel auto-encoder, which is able to jointly encode the eigenmatrix and eigenvector into codewords. Simulation results show great performance improvement and robustness with extremely low overhead of the proposed EMEVNet method compared with the traditional DL-based CSI feedback methods.

Radio Frequency Fingerprint (RFF) identification on account of deep learning has the potential to enhance the security performance of wireless networks. Recently, several RFF datasets were proposed to satisfy requirements of large-scale datasets. However, most of these datasets are collected from 2.4G WiFi devices and through similar channel environments. Meanwhile, they only provided receiving data collected by the specific equipment. This paper utilizes software radio peripheral as a dataset generating platform. Therefore, the user can customize the parameters of the dataset, such as frequency band, modulation mode, antenna gain, and so on. In addition, the proposed dataset is generated through various and complex channel environments, which aims to better characterize the radio frequency signals in the real world. We collect the dataset at transmitters and receivers to simulate a real-world RFF dataset based on the long-term evolution (LTE). Furthermore, we verify the dataset and confirm its reliability. The dataset and reproducible code of this paper can be downloaded from GitHub link: https://github.com/njuptzsp/XSRPdataset.

Millimeter wave (mmWave) communication technique has been developed rapidly because of many advantages of high speed, large bandwidth, and ultra-low delay. However, mmWave communications systems suffer from fast fading and frequent blocking. Hence, the ideal communication environment for mmWave is line of sight (LOS) channel. To improve the efficiency and capacity of mmWave system, and to better build the Internet of Everything (IoE) service network, this paper focuses on the channel identification technique in line-of- sight (LOS) and non-LOS (NLOS) environments. Considering the limited computing ability of user equipments (UEs), this paper proposes a novel channel identification architecture based on eigen features, i.e. eigenmatrix and eigenvector (EMEV) of channel state information (CSI). Furthermore, this paper explores clustered delay line (CDL) channel identification with mmWave, which is defined by the 3rd generation partnership project (3GPP). Ther experimental results show that the EMEV based scheme can achieve identification accuracy of 99.88% assuming perfect CSI. In the robustness test, the maximum noise can be tolerated is SNR= 16 dB, with the threshold acc \geq 95%. What is more, the novel architecture based on EMEV feature will reduce the comprehensive overhead by about 90%.

Given a smooth bounded domain $\Omega$ in $\mathbb{R}^2$, we study the following anisotropic Neumann problem $$ \begin{cases} -\nabla(a(x)\nabla u)+a(x)u=\lambda a(x) u^{p-1}e^{u^p},\,\,\,\, u>0\,\,\,\,\, \textrm{in}\,\,\,\,\, \Omega,\\[2mm] \frac{\partial u}{\partial\nu}=0\,\, \qquad\quad\qquad\qquad\qquad\qquad\qquad \ \ \ \ \,\qquad\quad\, \textrm{on}\,\,\, \partial\Omega, \end{cases} $$ where $\lambda>0$ is a small parameter, $0

Let $\Omega$ be a bounded domain in $\mathbb{R}^2$ with smooth boundary, we study the following anisotropic elliptic Neumann problem with Hardy-H\'{e}non weight $$ \begin{cases} -\nabla(a(x)\nabla u)+a(x)u=a(x)|x-q|^{2\alpha}u^p,\,\,\,\, u>0\,\,\,\,\, \textrm{in}\,\,\,\,\, \Omega,\\[2mm] \frac{\partial u}{\partial\nu}=0\,\, \qquad\quad\qquad\qquad\qquad \qquad\qquad\qquad\qquad \,\ \ \,\,\,\, \textrm{on}\,\,\, \partial\Omega, \end{cases} $$ where $\nu$ denotes the outer unit normal vector to $\partial\Omega$, $q\in\overline{\Omega}$, $\alpha\in(-1,+\infty)\setminus\mathbb{N}$, $p>1$ is a large exponent and $a(x)$ is a positive smooth function. We investigate the effect of the interaction between anisotropic coefficient $a(x)$ and singular source $q$ on the existence of concentrating solutions. We show that if $q\in\Omega$ is a strict local maximum point of $a(x)$, there exists a family of positive solutions with arbitrarily many interior spikes accumulating to $q$; while if $q\in\partial\Omega$ is a strict local maximum point of $a(x)$ and satisfies $\langle\nabla a(q),\,\nu(q)\rangle=0$, such a problem has a family of positive solutions with arbitrarily many mixed interior and boundary spikes accumulating to $q$. In particular, we find that concentration at singular source $q$ is always possible whether $q\in\overline{\Omega}$ is an isolated local maximum point of $a(x)$ or not., Comment: This manuscript has been accepted for publication in Topological Methods in Nonlinear Analysis(TMNA). arXiv admin note: text overlap with arXiv:1904.02936

Let $\Omega$ be a bounded domain in $\mathbb{R}^2$ with smooth boundary, we study the following elliptic Dirichlet problem $$ \begin{cases} -\Delta\upsilon= e^{\upsilon}-s\phi_1-4\pi\alpha\delta_p-h(x)\,\,\,\, \,\textrm{in}\,\,\,\,\,\Omega,\\[2mm] \upsilon=0 \quad\quad\quad\quad\quad\quad \qquad\qquad\quad\quad\,\,\,\, \textrm{on}\,\ \,\partial\Omega, \end{cases} $$ where $s>0$ is a large parameter, $h\in C^{0,\gamma}(\overline{\Omega})$, $p\in\Omega$, $\alpha\in(-1,+\infty)\setminus\mathbb{N}$, $\delta_p$ denotes the Dirac measure supported at point $p$ and $\phi_1$ is a positive first eigenfunction of the problem $-\Delta\phi=\lambda\phi$ under Dirichlet boundary condition in $\Omega$. If $p$ is a strict local maximum point of $\phi_1$, we show that such a problem has a family of solutions $\upsilon_s$ with arbitrary $m$ bubbles accumulating to $p$, and the quantity $\int_{\Omega}e^{\upsilon_s}\rightarrow8\pi(m+1+\alpha)\phi_1(p)$ as $s\rightarrow+\infty$., Comment: This manuscript has been accepted for publication in Advances in Differential Equations

Given a smooth bounded domain $\mathcal{D}$ in $\mathbb{R}^N$ with $N\geq3$, we study the existence and the profile of positive solutions for the following elliptic Nenumann problem $$\begin{cases}-\Delta \upsilon+\upsilon=\upsilon^p,\,\quad \upsilon>0 \quad\textrm{in}\ \mathcal{D},\\[1mm] \frac{\partial \upsilon}{\partial\nu}=0\qquad\qquad\qquad\qquad \textrm{on}\ \partial\mathcal{D}, \end{cases}$$ where $p>1$ is a large exponent and $\nu$ denotes the outer unit normal vector to the boundary $\partial\mathcal{D}$. For suitable domains $\mathcal{D}$, by a constructive way we prove that, for any non-negative integers $k$, $l$ with $k+l\geq1$, if $p$ is large enough, such a problem has a family of positive solutions with $k$ boundary layers and $l$ interior layers which concentrate along $k+l$ distinct $(N-2)$-dimensional minimal submanifolds of $\partial\mathcal{D}$, or collapse to the same $(N-2)$-dimensional minimal submanifold of $\partial\mathcal{D}$ as $p\rightarrow+\infty$., Comment: This manuscript has been accepted for publication in Communications in Contemporary Mathematics