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Existence results for fractional Brezis-Nirenberg type problems in unbounded domains 无界区域上分数阶Brezis-Nirenberg型问题的存在性结果
IF 0.7 4区 数学 Q2 MATHEMATICS Pub Date : 2022-12-10 DOI: 10.12775/tmna.2022.009
Yansheng Shen, Xumin Wang
In this paper we study the fractional Brezis-Nirenberg type problems in unbounded cylinder-type domainsbegin{align*}begin{cases}(-Delta)^{s}u-mudfrac{u}{|x|^{2s}}=lambda u+|u|^{2^{ast}_{s}-2}u & text{in } Omega, u=0 & text{in } mathbb{R}^{N}setminus Omega,end{cases}end{align*}where $(-Delta)^{s}$ is the fractional Laplace operator with $sin(0,1)$,$muin[0,Lambda_{N,s})$ with $Lambda_{N,s}$ the best fractional Hardy constant, $lambda> 0$, $N> 2s$ and $2^{ast}_{s}={2N}/({N-2s})$denotes the fractional critical Sobolev exponent. By applying the fractionalPoincaré inequality together with the concentration-compactness principlefor fractional Sobolev spaces in unbounded domains, we prove an existenceresult to the equation.
本文研究了无界圆柱型域中的分数阶Brezis-Nirenberg型问题^{s}u-mudfrac{u}{|x|^{2s}}=λu+| u | ^{2^{ast}_{s}-2}u&&text{in}Omega,u=0&&text{in}mathbb{R}^{N}setminusOmega、end{cases}end{align*},其中$(-Delta)^{s}$是具有$sin(0,1)$的分数拉普拉斯算子,$muin[0],Lambda_{N,s})$,其中$Lambda_{N,s}$是最佳分式Hardy常数,$Lambda>0$,$N>2s$和$2^{sast}_{s}={2N}/({N-2s})$$表示分数临界Sobolev指数。
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引用次数: 0
Time-dependent global attractors for the strongly damped wave equations with lower regular forcing term 低正则强迫项强阻尼波动方程的时变全局吸引子
IF 0.7 4区 数学 Q2 MATHEMATICS Pub Date : 2022-12-10 DOI: 10.12775/tmna.2022.022
Xinyu Mei, T. Sun, Yongqin Xie, Kaixuan Zhu
In this paper, based on a new theoretical framework oftime-dependent global attractors (Conti, Pata and Temam cite{CPT13}),we consider the strongly damped wave equations $varepsilon(t)u_{tt}-Delta u_{t}-Delta u+f(u)=g(x)$and establish the existence of attractorsin $mathcal{H}_{t}=H_{0}^{1}(Omega)times L^{2}(Omega)$and $mathcal{V}_{t}=H_{0}^{1}(Omega)times H_{0}^{1}(Omega)$, respectively.
本文基于一个新的时变全局吸引子理论框架(Conti, Pata和Temam cite{CPT13}),考虑了强阻尼波动方程$varepsilon(t)u_{tt}-Delta u_{t}-Delta u+f(u)=g(x)$,并分别在$mathcal{H}_{t}=H_{0}^{1}(Omega)times L^{2}(Omega)$和$mathcal{V}_{t}=H_{0}^{1}(Omega)times H_{0}^{1}(Omega)$中建立了吸引子的存在性。
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引用次数: 0
A note on local minimizers of energy on complete manifolds 关于完全流形上能量的局部极小值的注记
IF 0.7 4区 数学 Q2 MATHEMATICS Pub Date : 2022-12-10 DOI: 10.12775/tmna.2022.013
M. Batista, José I. Santos
In this paper, we study the geometric rigidity of complete Riemannian manifolds admitting local minimizers of energy functionals.More precisely, assuming the existence of a non-trivial local minimizer and under suitable assumptions, a Riemannian manifold under consideration must bea product manifold furnished with a warped metric.Secondly, under similar hypotheses, we deduce a geometrical splitting inthe same fashion as in the Cheeger-Gromoll splitting theorem and we also get information about local minimizers.
在本文中,我们研究了完全黎曼流形的几何刚度,它允许能量泛函的局部极小值。更准确地说,假设存在一个非平凡的局部极小子,并且在适当的假设下,所考虑的黎曼流形必须是一个具有翘曲度量的乘积流形。其次,在类似的假设下,我们以与Cheeger-Gromoll分裂定理相同的方式推导了几何分裂,并且我们还得到了关于局部极小值的信息。
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引用次数: 1
On a semilinear fourth order elliptic problem with asymmetric nonlinearity 一类具有非对称非线性的半线性四阶椭圆型问题
IF 0.7 4区 数学 Q2 MATHEMATICS Pub Date : 2022-12-10 DOI: 10.12775/tmna.2022.028
Fabiana Ferreira, E. Medeiros, Wallisom Rosa
In this work, we address the existence of solutions for a biharmonic elliptic equation with homogeneous Navier boundary condition. The problem is asymmetric and has linear behavior on $-infty$ and superlinear on $+infty$. To obtain the results we apply topological methods.
在这项工作中,我们讨论了具有齐次Navier边界条件的双调和椭圆方程解的存在性。该问题是不对称的,在$-infty$上具有线性行为,在$+infty$中具有超线性行为。为了获得结果,我们应用拓扑方法。
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引用次数: 0
Periodic solutions of fractional Laplace equations: Least period, axial symmetry and limit 分数阶拉普拉斯方程的周期解:最小周期,轴对称和极限
IF 0.7 4区 数学 Q2 MATHEMATICS Pub Date : 2022-12-10 DOI: 10.12775/tmna.2022.016
Zhenping Feng, Zhuoran Du
We are concerned with periodic solutions of the fractional Laplace equationbegin{equation*}{(-partial_{xx})^s}u(x)+F'(u(x))=0 quad mbox{in }mathbb{R},end{equation*}where $0< s< 1$. The smooth function $F$ is a double-well potential with wells at$+1$ and $-1$. We show that the value of least positive period is$2{pi}times({1}/{-F''(0)})^{{1}/({2s})}$. The axial symmetry of odd periodic solutions is obtained by moving plane method.We also prove that odd periodic solutions $u_{T}(x)$ converge to a layer solution of the same equation as periods $Trightarrow+infty$.
我们关注分数阶拉普拉斯方程的周期解 begin{equation*}{(-partial_{xx})^s}u(x)+F’(u(x。光滑函数$F$是具有$+1$和$-1$阱的双阱势。我们证明了最小正周期的值是$2{pi}times({1}/{-F‘'(0)})^{1}/({2s})}$。利用移动平面法得到了奇周期解的轴对称性。我们还证明了奇周期解$u_{T}(x)$收敛于与周期$Trightarrow+infty$相同的方程的层解。
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引用次数: 0
Some existence results for elliptic systems with exponential nonlinearities and convection terms in dimension two 具有指数非线性和二维对流项的椭圆系统的一些存在性结果
IF 0.7 4区 数学 Q2 MATHEMATICS Pub Date : 2022-12-10 DOI: 10.12775/tmna.2022.025
W. Liu
In this paper, we establish the existence of solutions to a class of elliptic systems.The nonlinearities include exponential growth terms and convection terms. The exponential growth term means it could be critical growth at $infty$.The Trudinger-Moser inequality is used to deal with it. The convection term means it involves the gradient of unknown function.The strong convergence of sequences is employed to overcome the difficulties caused by convection terms.The variational methods are invalid and the Galerkin method and an approximation scheme are applied to obtain four different solutions.Our results supplements those from cite{Araujo2018}.
本文证明了一类椭圆系统解的存在性。非线性包括指数增长项和对流项。指数增长项意味着它可能是$infty$的临界增长。使用Trudinger-Moser不等式来处理它。对流项意味着其涉及未知函数的梯度。利用序列的强收敛性来克服对流项带来的困难。变分方法是无效的,并且应用Galerkin方法和近似格式来获得四种不同的解。我们的结果补充了cite{Araujo2018}的结果。
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引用次数: 0
A-priori bound and Hölder continuity of solutions to degenerate elliptic equations with variable exponents 退化变指数椭圆方程解的先验界和Hölder连续性
IF 0.7 4区 数学 Q2 MATHEMATICS Pub Date : 2022-12-10 DOI: 10.12775/tmna.2022.021
Ky Ho, L. Nhan, L. Truong
We investigate the boundedness and regularity of solutions to degenerate elliptic equations with variable exponents that are subject to the Dirichlet boundary condition. By employing the De Giorgi iteration, we obtain a-priori bounds and the Hölder continuity for solutions. As an application, we obtain the existence of infinitely many small solutions for a class of degenerate elliptic equations involving variable exponents.
研究了易指数退化椭圆型方程在Dirichlet边界条件下解的有界性和正则性。利用De Giorgi迭代,得到了解的先验界和Hölder连续性。作为一个应用,我们得到了一类变指数退化椭圆型方程无穷小解的存在性。
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引用次数: 0
Affine-periodic solutions for generalized ODEs and other equations 广义微分方程及其它方程的仿射周期解
IF 0.7 4区 数学 Q2 MATHEMATICS Pub Date : 2022-12-10 DOI: 10.12775/tmna.2022.027
M. Federson, R. Grau, Carolina Mesquita
It is known that the concept of affine-periodicity encompasses classic notionsof symmetries as the classic periodicity, anti-periodicity and rotating symmetries(in particular, quasi-periodicity). The aim of this paper is to establish the basis of affine-periodic solutions of generalized ODEs. Thus, for a given real number $T> 0$ and an invertible $ntimes n$ matrix $Q$, with entries in $mathbb C$,we establish conditions for the existence of a $(Q,T)$-affine-periodic solutionwithin the framework of nonautonomous generalized ODEs, whose integral form displays the nonabsolute Kurzweil integral, which encompasses many typesof integrals, such as the Riemann, the Lebesgue integral, among others. The main tools employed here are the fixed point theorems of Banach and of Krasnosel'skiĭ.We apply our main results to measure differential equations withHenstock-Kurzweil-Stiejtes righthand sides as well as to impulsive differential equations and dynamic equations on time scales which are particular cases of the former.
众所周知,仿射周期性的概念包含了经典的对称性概念,如经典周期性、反周期性和旋转对称性(特别是准周期性)。本文的目的是建立广义微分方程仿射周期解的基础。因此,对于给定的实数$ t> $和一个可逆的$n乘以n$矩阵$Q$,在$mathbb C$中,我们建立了在非自治广义微分方程框架内$(Q,T)$-仿射周期解存在的条件,其积分形式表现为非绝对Kurzweil积分,它包含许多类型的积分,如Riemann积分,Lebesgue积分等。这里使用的主要工具是Banach和Krasnosel的不动点定理。我们将我们的主要结果应用于测量henstock - kurzweil - stiejtes右边的微分方程,以及脉冲微分方程和时间尺度上的动态方程,这是前者的特殊情况。
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引用次数: 1
Impact of the Alberta Stroke Program CT Score subregions on long-term functional outcomes in acute ischemic stroke: Results from two multicenter studies in China. 阿尔伯塔省卒中项目 CT 评分亚区对急性缺血性卒中长期功能预后的影响:中国两项多中心研究的结果。
IF 4.9 4区 数学 Q2 MATHEMATICS Pub Date : 2022-11-15 eCollection Date: 2024-04-01 DOI: 10.2478/jtim-2022-0057
Xinrui Wang, Caohui Duan, Jinhao Lyu, Dongshan Han, Kun Cheng, Zhihua Meng, Xiaoyan Wu, Wen Chen, Guohua Wang, Qingliang Niu, Xin Li, Yitong Bian, Dan Han, Weiting Guo, Shuai Yang, Ximing Wang, Tijiang Zhang, Junying Bi, Feiyun Wu, Shuang Xia, Dan Tong, Kai Duan, Zhi Li, Rongpin Wang, Jinan Wang, Xin Lou

Background and objectives: The Alberta Stroke Program CT Score (ASPECTS) is a widely used rating system for assessing infarct extent and location. We aimed to investigate the prognostic value of ASPECTS subregions' involvement in the long-term functional outcomes of acute ischemic stroke (AIS).

Materials and methods: Consecutive patients with AIS and anterior circulation large-vessel stenosis and occlusion between January 2019 and December 2020 were included. The ASPECTS score and subregion involvement for each patient was assessed using posttreatment magnetic resonance diffusion-weighted imaging. Univariate and multivariable regression analyses were conducted to identify subregions related to 3-month poor functional outcome (modified Rankin Scale scores, 3-6) in the reperfusion and medical therapy cohorts, respectively. In addition, prognostic efficiency between the region-based ASPECTS and ASPECTS score methods were compared using receiver operating characteristic curves and DeLong's test.

Results: A total of 365 patients (median age, 64 years; 70% men) were included, of whom 169 had poor outcomes. In the reperfusion therapy cohort, multivariable regression analyses revealed that the involvement of the left M4 cortical region in left-hemisphere stroke (adjusted odds ratio [aOR] 5.39, 95% confidence interval [CI] 1.53-19.02) and the involvement of the right M3 cortical region in right-hemisphere stroke (aOR 4.21, 95% CI 1.05-16.78) were independently associated with poor functional outcomes. In the medical therapy cohort, left-hemisphere stroke with left M5 cortical region (aOR 2.87, 95% CI 1.08-7.59) and caudate nucleus (aOR 3.14, 95% CI 1.00-9.85) involved and right-hemisphere stroke with right M3 cortical region (aOR 4.15, 95% CI 1.29-8.18) and internal capsule (aOR 3.94, 95% CI 1.22-12.78) affected were related to the increased risks of poststroke disability. In addition, region-based ASPECTS significantly improved the prognostic efficiency compared with the conventional ASPECTS score method.

Conclusion: The involvement of specific ASPECTS subregions depending on the affected hemisphere was associated with worse functional outcomes 3 months after stroke, and the critical subregion distribution varied by clinical management. Therefore, region-based ASPECTS could provide additional value in guiding individual decision making and neurological recovery in patients with AIS.

背景和目的:阿尔伯塔省卒中计划 CT 评分(ASPECTS)是一种广泛使用的评估梗死范围和位置的评分系统。我们旨在研究 ASPECTS 亚区域参与急性缺血性卒中(AIS)长期功能预后的预后价值:纳入2019年1月至2020年12月期间连续收治的AIS和前循环大血管狭窄和闭塞患者。使用治疗后磁共振弥散加权成像评估每位患者的 ASPECTS 评分和亚区受累情况。通过单变量和多变量回归分析,分别确定了再灌注组和药物治疗组中与3个月不良功能预后(改良Rankin量表评分,3-6分)相关的亚区。此外,还使用接收器操作特征曲线和 DeLong 检验比较了基于区域的 ASPECTS 和 ASPECTS 评分方法的预后效率:结果:共纳入了 365 名患者(中位年龄 64 岁,70% 为男性),其中 169 人预后不佳。在再灌注治疗队列中,多变量回归分析显示,左半球脑卒中患者左侧 M4 皮质区域受累(调整赔率比 [aOR] 5.39,95% 置信区间 [CI]1.53-19.02)和右半球脑卒中患者右侧 M3 皮质区域受累(aOR 4.21,95% CI 1.05-16.78)与不良功能预后独立相关。在药物治疗队列中,左半球卒中左侧 M5 皮质区(aOR 2.87,95% CI 1.08-7.59)和尾状核(aOR 3.14,95% CI 1.00-9.85)受累以及右半球卒中右侧 M3 皮质区(aOR 4.15,95% CI 1.29-8.18)和内囊(aOR 3.94,95% CI 1.22-12.78)受累与卒中后残疾风险增加有关。此外,与传统的 ASPECTS 评分方法相比,基于区域的 ASPECTS 能显著提高预后效率:结论:受累半球的特定 ASPECTS 亚区受累与卒中后 3 个月功能预后较差有关,关键亚区的分布因临床治疗而异。因此,基于区域的 ASPECTS 可为 AIS 患者的个体决策和神经功能恢复提供额外的指导价值。
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引用次数: 0
A word on Professor Kazimierz Goebel (1940-2022) 卡齐米兹·戈贝尔教授(1940-2022)
IF 0.7 4区 数学 Q2 MATHEMATICS Pub Date : 2022-09-24 DOI: 10.12775/tmna.2022.019
Stanisław Prus
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引用次数: 0
期刊
Topological Methods in Nonlinear Analysis
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