Existence of weak solutions for quasilinear Schrödinger equations with a parameter

In this paper, we study the following quasilinear Schrödinger equation of the form −∆pu + V(x)|u| p−2u − h ∆p(1 + u 2 α/2i αu 2(1 + u 2) (2−α)/2 = k(u), x ∈ R N, where p-Laplace operator ∆pu = div(|∇u| p−2∇u) (1 < p ≤ N) and α ≥ 1 is a parameter. Under some appropriate assumptions on the potential V and the nonlinear term k, using some special techniques, we establish the existence of a nontrivial solution in C 1,β loc (RN) (0 < β < 1), we also show that the solution is in L ∞(RN) and decays to zero at infinity when 1 < p < N

Existence of weak solutions for quasilinear Schrödinger equations with a parameter

In this paper, we study the following quasilinear Schrödinger equation of the form \begin{equation*} -\Delta_{p}u+V(x)|u|^{p-2}u-\left[\Delta_{p}(1+u^{2})^{\alpha/2}\right]\frac{\alpha u}{2(1+u^{2})^{(2-\alpha)/2}}=k(u),\qquad x\in \mathbb{R}^{N}, \end{equation*} where $p$-Laplace operator $\Delta_{p}u={\rm div}(|\nabla u|^{p-2}\nabla u)\ (1<p\leq N)$ and $\alpha\geq1$ is a parameter. Under some appropriate assumptions on the potential $V$ and the nonlinear term $k$, using some special techniques, we establish the existence of a nontrivial solution in $C_{\rm loc}^{1,\beta}(\mathbb{R}^{N})\ (0<\beta<1),$ we also show that the solution is in $L^{\infty}(\mathbb{R}^{N})$ and decays to zero at infinity when $1<p<N$

On finite-time anti-saturated proximity control with a tumbling non-cooperative space target

For the challenging problem that a spacecraft approaching a tumbling target with non-cooperative maneuver, an anti-saturated proximity control method is proposed in this paper. First, a brand-new appointed-time convergent performance function is developed via exploring Bezier curve to quantitatively characterize the transient and steady-state behaviors of the pose tracking error system. The major advantage of the proposed function is that the actuator saturation phenomenon at the beginning can be effectively reduced. Then, an anti-saturated pose tracking controller is devised along with an adaptive saturation compensator. Wherein, the finite-time stability of both the pose and its velocity error signals are guaranteed simultaneously in the presence of actuator saturation. Finally, two groups of illustrative examples are organized and verify that the close-range proximity is effectively realized even with unknown target maneuver

Electrospun ZnO–SnO2 Composite Nanofibers and Enhanced Sensing Properties to SF6 Decomposition Byproduct H2S

Hydrogen sulfide (H2S) is an important decomposition component of sulfur hexafluoride (SF6), which has been extensively used in gas-insulated switchgear (GIS) power equipment as insulating and arc-quenching medium. In this work, electrospun ZnO-SnO2 composite nanofibers as a promising sensing material for SF6 decomposition component H2S were proposed and prepared. The crystal structure and morphology of the electrospun ZnO-SnO2 samples were investigated by X-ray diffraction (XRD), scanning electron microscopy (SEM) and transmission electron microscopy (TEM), respectively. The composition of the sensitive materials was analyzed by energy dispersive X-ray spectrometers (EDS) and X-ray photoelectron spectroscopy (XPS). Side heated sensors were fabricated with the electrospun ZnO-SnO2 nanofibers and the gas sensing behaviors to H2S gas were systematically investigated. The proposed ZnO–SnO2 composite nanofibers sensor showed lower optimal operating temperature, enhanced sensing response, quick response/recovery time and good long-term stability against H2S. The measured optimal operating temperature of the ZnO–SnO2 nanofibers sensor to 50 ppm H2S gas was about 250°C with a response of 66.23, which was 6 times larger than pure SnO2 nanofibers sensor. The detection limit of the fabricated ZnO–SnO2 nanofibers sensor toward H2S gas can be as low as 0.5 ppm. Finally, a plausible sensing mechanism for the proposed ZnO–SnO2 composite nanofibers sensor to H2S was also discussed

Multiplicity of solutions for a class of fractional p-Kirchhoff system with sign-changing weight functions

Abstract In this paper, we investigate the fractional p-Kirchhoff -type system: {M(∫R2N|u(x)−u(y)|p|x−y|N+psdxdy)(−Δ)psu=μg(x)|u|β−2u+aa+bh(x)|u|a−2u|v|b,in Ω,M(∫R2N|v(x)−v(y)|p|x−y|N+psdxdy)(−Δ)psv=σf(x)|v|β−2v+ba+bh(x)|v|b−2v|u|a,in Ω,u=v=0,in RN∖Ω, \begin{aligned} \textstyle\begin{cases} M (\int_{{ \mathbb {R} }^{2N}}\frac{\vert u(x)-u(y) \vert ^{p}}{\vert x-y \vert ^{N+ps}}\,dx\,dy )(- \Delta )^{s}_{p}u=\mu g(x)\vert u \vert ^{\beta -2}u+\frac{a}{a+b}h(x)\vert u \vert ^{a-2}u\vert v \vert ^{b},&\mbox{in } \Omega , \\ M (\int_{{ \mathbb {R} }^{2N}}\frac{\vert v(x)-v(y) \vert ^{p}}{\vert x-y \vert ^{N+ps}}\,dx\,dy )(- \Delta )^{s}_{p}v=\sigma f(x)\vert v \vert ^{\beta -2}v+\frac{b}{a+b}h(x)\vert v \vert ^{b-2}v\vert u \vert ^{a},&\mbox{in } \Omega , \\ u=v=0,&\mbox{in } { \mathbb {R} }^{N}\setminus \Omega , \end{cases}\displaystyle \end{aligned} where Ω⊂RN $\Omega \subset \mathbb{R}^{N}$ is a smooth bounded domain, (−Δ)ps $(-\Delta )^{s}_{p}$ is the fractional p-Laplacian operator with 01 $a>1$, b>1 $b>1$ satisfy 20 $k>0$, λ, τ≥0 $\tau \geq 0$, τ=0 $\tau =0$ if and only if λ=0 $\lambda =0$. The weight functions g, f, h change sign in Ω and satisfy suitable conditions. By using the Nehari manifold method, it is proved that the system has at least two solutions provided that 2λ1 $\lambda >\lambda_{1}$ under the assumptions μ=σ=0 $\mu =\sigma =0$ and p<a+b<min{p(τ+1),ps∗} $p< a+b<\min \{p(\tau +1),p_{s}^{*}\}$

Parameter-Independent Event-Triggered Implicit UKF for the Celestial Navigation Using Time Delay Measurement

Celestial navigation using time delay measurement is an innovative autonomous navigation method. To calculate the equivalent measurement, the numerical method needs to be applied, which is time-consuming. The event-triggered mechanism intermittently and aperiodically processes measurements by judging if the update error has changed drastically. However, its performance is greatly affected by the constant threshold. To solve this problem, a parameter-independent event-triggered implicit unscented Kalman filter (UKF) is proposed and applied to the celestial navigation using time delay measurement. The innovation at the current moment and the updated estimate covariance at the last moment are compared with the previous value instead of the constant threshold. The event is automatically triggered when the accuracy of the state estimate is low. Simulation results indicate that the proposed parameter-independent event-triggered implicit UKF can reduce the running time by reducing unnecessary measurement updates, whose performance will not be affected by any parameter or window size. In a word, the proposed method substitutes the dynamic threshold for the constant threshold, ensuring that its performance will not be affected by any parameter or window size

PCA-Based Denoising Algorithm for Outdoor Lidar Point Cloud Data

Due to the complexity of surrounding environments, lidar point cloud data (PCD) are often degraded by plane noise. In order to eliminate noise, this paper proposes a filtering scheme based on the grid principal component analysis (PCA) technique and the ground splicing method. The 3D PCD is first projected onto a desired 2D plane, within which the ground and wall data are well separated from the PCD via a prescribed index based on the statistics of points in all 2D mesh grids. Then, a KD-tree is constructed for the ground data, and rough segmentation in an unsupervised method is conducted to obtain the true ground data by using the normal vector as a distinctive feature. To improve the performance of noise removal, we propose an elaborate K nearest neighbor (KNN)-based segmentation method via an optimization strategy. Finally, the denoised data of the wall and ground are spliced for further 3D reconstruction. The experimental results show that the proposed method is efficient at noise removal and is superior to several traditional methods in terms of both denoising performance and run speed

Robust Optimal Dispatch of AC/DC Hybrid Microgrids Considering Generation and Load Uncertainties and Energy Storage Loss

Uncertainties from multiple generation resources and loads have introduced tremendous challenges to the optimal dispatch of microgrids. This paper presents a novel two-stage min-max-min robust optimal dispatch model for a representative islanded AC/DC hybrid microgrid that faces uncertainties in renewable energy generation and customer loads. The first stage of the model determines the startup/shutdown state of the diesel engine generator and the operating state of the bi-directional converter of the microgrid. Then, the second stage optimizes the power dispatch of individual units in the microgrid. A new linearized equipment cost model is developed, counting for the degradation of energy storage. The use of this linear model helps maintain the linearity of objective function without compromising the solution accuracy. The column-and-constraint generation algorithm is implemented to efficiently obtain a robust dispatching plan for the microgrid, which minimizes the daily operating cost in the worst-case scenario. A case study and sensitivity analyses further demonstrate the rationale and the unique capability of the proposed model for planning the operation of AC/DC hybrid microgrids