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Halpern-type proximal point algorithm in CAT(0) spaces CAT(0)空间中的halpern型近点算法
IF 0.7 4区 数学 Q2 MATHEMATICS Pub Date : 2023-07-16 DOI: 10.12775/tmna.2022.038
C. C. Okeke
A method which is a combination of the Halpern method and proximal point method(PPA) is introduced in this paper. It is proved that the sequence of iterates generated by our method converges strongly to a point which is a common solution to some monotone inclusion problem and fixed point problem in CAT$(0)$ spaces under some appropriate conditions.
本文介绍了一种将Halpern法和近点法相结合的方法。证明了在适当的条件下,我们方法生成的迭代序列强收敛于CAT$(0)$空间中某些单调包含问题和不动点问题的一个公共解。
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引用次数: 0
Convergence and well-posedness properties of uniformly locally contractive mappings 一致局部压缩映射的收敛性和适定性
IF 0.7 4区 数学 Q2 MATHEMATICS Pub Date : 2023-07-16 DOI: 10.12775/tmna.2022.035
S. Reich, A. Zaslavski
In a 1961 paper by E. Rakotch it was shown that a uniformly locally contractive mapping has a fixed point. In the present paper we show that for such a mapping, the fixed point problem is well posed and that inexact iterates of such a mapping converge to its unique fixed point, uniformly on bounded sets. Using the porosity notion, we also show that most uniformly locally nonexpansive mappings are, in fact, uniformly locally contractive.
E.Rakoch在1961年的一篇论文中证明了一致局部压缩映射具有不动点。在本文中,我们证明了对于这样的映射,不动点问题是适定的,并且这样的映射的不精确迭代在有界集上一致地收敛到它的唯一不动点。利用孔隙率的概念,我们还证明了大多数一致局部非扩张映射实际上是一致局部收缩的。
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引用次数: 0
Lower semicontinuity of Kirchhoff-type energy functionals and spectral gaps on (sub)Riemannian manifolds (次)黎曼流形上kirchhoff型能量泛函的下半连续性和谱隙
IF 0.7 4区 数学 Q2 MATHEMATICS Pub Date : 2023-07-16 DOI: 10.12775/tmna.2022.034
Csaba Farkas, S. Kajántó, C. Varga
In this paper we characterize the sequentially weakly lower semicontinuityof the parameter-depending energy functional associated with the critical Kirchhoffproblem in context of (sub)Riemannian manifolds.We also present some spectral gap and convexity results.
在(子)黎曼流形中,我们刻画了与临界Kirchhoff问题相关的依赖于参数的能量泛函的顺序弱下半连续性。我们还给出了一些谱间隙和凸性的结果。
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引用次数: 0
First record of the genus Pseudaeginella Mayer, 1890 (Crustacea, Amphipoda, Caprellidae) with a new species from Korean waters. Pseudaeginella Mayer, 1890 属(甲壳纲,两足目,栉水母科)的首次记录和来自韩国水域的一个新种。
IF 1.3 4区 数学 Q2 MATHEMATICS Pub Date : 2023-07-13 eCollection Date: 2023-01-01 DOI: 10.3897/zookeys.1169.105901
So-Yeon Shin, Chang-Mok Lee, Jun-Haeng Heo, Young-Hyo Kim

A new species of the genus Pseudaeginella Mayer, 1890 belonging to the family Caprellidae Leach, 1814 was collected from the South Sea in Korea. Pseudaeginellacarinaspinosasp. nov. is morphologically similar to related congeners belonging to the genera Paradeutella Mayer, 1890 and Pseudaeginella, in having dorsal projections on pereonites, triarticulate mandibular palp, small or absent molar, and uniarticulate pereopods 3 and 4. However, this new species is distinguished from its congeners by the position and size of dorsal projection. This is the first record of Pseudaeginella from the Northwest Pacific region, including Korea, and a key to species of the genus Pseudaeginella is also provided.

从韩国南海采集到一个属于 Caprellidae Leach, 1814 科 Pseudaeginella Mayer, 1890 属的新种。新种 Pseudaeginellacarinaspinosasp. 在形态上与 Paradeutella Mayer, 1890 属和 Pseudaeginella 属的相关同属种相似,都具有背侧突起、三节下颌腭、小臼齿或无臼齿以及单节第 3 和第 4 趾。不过,该新种与其同属种的区别在于背侧突的位置和大小。这是包括韩国在内的西北太平洋地区的第一个 Pseudaeginella 记录,同时还提供了 Pseudaeginella 属的物种检索表。
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引用次数: 0
Critical Kirchhoff-type equation with singular potential 具有奇异势的临界kirchhoff型方程
IF 0.7 4区 数学 Q2 MATHEMATICS Pub Date : 2023-06-23 DOI: 10.12775/tmna.2022.051
Yujian Su, Senli Liu
In this paper, we deal with the following Kirchhoff-type equation:begin{equation*}-bigg(1+int_{mathbb{R}^{3}}|nabla u|^{2}dxbigg)Delta u+frac{A}{|x|^{alpha}}u=f(u),quad xinmathbb{R}^{3},end{equation*}where $A> 0$ is a real parameter and $alphain(0,1)cup ({4}/{3},2)$.Remark that $f(u)=|u|^{2_{alpha}^{*}-2}u +lambda|u|^{q-2}u+|u|^{4}u$,where $lambda> 0$, $qin(2_{alpha}^{*},6)$,$2_{alpha}^{*}=2+{4alpha}/({4-alpha})$is the embedding bottom index, and $6$ is the embedding top index and Sobolev critical exponent.We point out that the nonlinearity $f$ is the almost ``optimal'' choice.First, for $alphain({4}/{3},2)$, applying the generalized version of Lions-type theorem and the Nehari manifold, we show the existence of nonnegativeNehari-type ground sate solution for above equation. Second, for $alphain(0,1)$, using the generalized version of Lions-type theorem and the Pohov{z}aev manifold, we establish the existence of nonnegative Pohov{z}aev-type groundstate solution for above equation. Based on our new generalized versionof Lions-type theorem, our works extend the results in Li-Su [Z. Angew. Math. Phys. {bf 66} (2015)].
在本文中,我们处理了以下Kirchhoff型方程:begin{方程*}-bigg(1+int_{mathbb{R}^{3}}|nabla u|^{2}dxbigg)Delta u+frac{A}{|x|^{alpha}}u=f(u),quad xinmathbb{R}^{3},end{方程*},其中$A>0$是实参数,$alphain(0,1)cup({4}/{3},2)$。注意$f(u|^{q-2}u+|u|^{4}u$,其中$lambda>0$,$qin(2_{alpha}^{*},6)$,$2_{aalpha}^{*}=2+{4alpha}/({4-alpha})$是嵌入底部索引,$6$是嵌入顶部索引和Sobolev临界指数。我们指出非线性$f$是几乎“最优”的选择。首先,对于({4}/{3},2)$中的$alpha,应用Lions型定理的广义形式和Nehari流形,我们证明了上述方程的非负Nehari型基态解的存在性。其次,对于$alphain(0,1)$,使用Lions型定理的广义版本和Pohov{z}aev流形,我们建立了非负Pohov的存在性{z}aev-type上述方程的基态解。基于我们新的Lions型定理的广义版本,我们的工作扩展了李素[Z.Angew.Math.Phys.{bf 66}(2015)]中的结果。
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引用次数: 0
Existence of nontrivial solutions to Schrödinger systems with linear and nonlinear couplings via Morse theory 基于Morse理论的线性和非线性耦合Schrödinger系统非平凡解的存在性
IF 0.7 4区 数学 Q2 MATHEMATICS Pub Date : 2023-06-23 DOI: 10.12775/tmna.2022.032
Zhitao Zhang, Meng Yu, Xiaotian Zheng
In this paper, we use Morse theory to study existence of nontrivial solutions to the following Schrödinger system with linear and nonlinear couplings which arises from Bose-Einstein condensates:$$begin{cases}-Delta u+lambda_{1} u+kappa v=mu_{1} u^{3}+beta uv^{2}& text{in } Omega,-Delta v+lambda_{2} v+kappa u=mu_{2} v^{3}+beta vu^{2}& text{in } Omega,u=v=0 & text{on } partialOmega,end{cases}$$where $Omega$ is a bounded smooth domain in $mathbb{R}^{N}$($N=2,3$),$lambda_{1},lambda_{2},mu_{1},mu_{2} in mathbb{R} setminus { 0 }$,$beta, kappa in mathbb{R}$. In two cases of$kappa=0$ and $kappaneq 0$, by transferring an eigenvalue problem into an algebraic problem, we compute the Morse index and critical groups of the trivial solution. Furthermore, even when the trivial solution is degenerate,we show a local linking structure of energy functional at zero within a suitable parameter range and then get critical groups of the trivial solution.As an application, we use Morse theory to get an existence theorem on existenceof nontrivial solutions under some conditions.
本文利用莫尔斯理论研究了以下由玻色-爱因斯坦凝聚引起的具有线性和非线性耦合的Schrödinger系统的非平凡解的存在性:$$begin{cases}-Delta u+lambda_{1} u+kappa v=mu_{1} u^{3}+beta uv^{2}& text{in } Omega,-Delta v+lambda_{2} v+kappa u=mu_{2} v^{3}+beta vu^{2}& text{in } Omega,u=v=0 & text{on } partialOmega,end{cases}$$其中$Omega$是$mathbb{R}^{N}$ ($N=2,3$), $lambda_{1},lambda_{2},mu_{1},mu_{2} in mathbb{R} setminus { 0 }$, $beta, kappa in mathbb{R}$中的有界光滑域。在$kappa=0$和$kappaneq 0$两种情况下,通过将特征值问题转化为代数问题,我们计算了平凡解的莫尔斯指数和临界群。进一步,当平凡解是简并解时,在适当的参数范围内给出了一个能量泛函于零的局部连接结构,从而得到了平凡解的临界群。作为应用,我们利用Morse理论得到了在某些条件下非平凡解的存在性定理。
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引用次数: 0
Multiple solutions to Bahri-Coron problem involving fractional $p$-Laplacian in some domain with nontrivial topology 非平凡拓扑域上涉及分数阶拉普拉斯算子的Bahri-Coron问题的多重解
IF 0.7 4区 数学 Q2 MATHEMATICS Pub Date : 2023-06-23 DOI: 10.12775/tmna.2022.033
Uttam Kumar, Sweta Tiwari
In this article, we establish the existence of positive and multiple sign-changing solutions to the fractional $p$-Laplacian equation with purely critical nonlinearity begin{equation}label{Ppomegas-a}tag{P$_{p,Omega}^{s}$}begin{cases} (-Delta)_{p}^s u =|u|^{p_s^*-2} u& text{in }Omega, u =0 & text{on }Omega^{c}, end{cases}end{equation}in a bounded domain $Omegasubset mathbb{R}^{N}$ for $sin (0,1)$,$pin (1,infty)$, and the fractional critical Sobolev exponent$p^{*}_{s}={Np}/({N-sp})$ under some symmetry assumptions.We study Struwe's type global compactness results for the Palais-Smale sequencein the presence of symmetries.
在某些对称假设下,我们建立了具有纯临界非线性begin{equation}label{Ppomegas-a}tag{P$_{p,Omega}^{s}$}begin{cases} (-Delta)_{p}^s u =|u|^{p_s^*-2} u& text{in }Omega, u =0 & text{on }Omega^{c}, end{cases}end{equation}的分数阶$p$ - laplace方程在有界域$Omegasubset mathbb{R}^{N}$上($sin (0,1)$, $pin (1,infty)$)和分数阶临界Sobolev指数$p^{*}_{s}={Np}/({N-sp})$的正解和多重变号解的存在性。研究了存在对称性的palais - small序列的Struwe型全局紧性结果。
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引用次数: 0
Multiplicity of positive solutions for a Kirchhoff type problem without asymptotic conditions 无渐近条件的Kirchhoff型问题正解的多重性
IF 0.7 4区 数学 Q2 MATHEMATICS Pub Date : 2023-06-23 DOI: 10.12775/tmna.2022.031
X. Qian
In this paper, we are concerned with the multiplicity of positive solutions for the following Kirchhoff type problem[begin{cases}-bigg({varepsilon}^2a+{varepsilon}bint_{mathbb{R}^3} |n u|^2dxbigg)Delta u+u=Q(x)|u|^{p-2}u, & xinmathbb{R}^3,uin H^1big(mathbb{R}^3big), quad u> 0, & xinmathbb{R}^3,end{cases}]where $varepsilon> 0$ is a small parameter, $a,b> 0$ are constants, $4< p< 6$, $Q$ is a nonnegative continuous potential and does not satisfy any asymptotic condition. Combining Nehari manifold and concentration compactness principle, we study how the shape of the graph of $Q(x)$ affects the number of positive solutions.
本文研究了下述Kirchhoff型问题[begin{cases}-bigg({varepsilon}^2a+{varepsilon}bint_{mathbb{R}^3} |n u|^2dxbigg)Delta u+u=Q(x)|u|^{p-2}u, & xinmathbb{R}^3,uin H^1big(mathbb{R}^3big), quad u> 0, & xinmathbb{R}^3,end{cases}]的正解的多重性,其中$varepsilon> 0$是一个小参数,$a,b> 0$是常数,$4< p< 6$, $Q$是一个不满足任何渐近条件的非负连续势。结合Nehari流形和集中紧致原理,研究了$Q(x)$图的形状对正解个数的影响。
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引用次数: 0
On the relative category in the brake orbits problem 关于制动轨道问题中的相对范畴
IF 0.7 4区 数学 Q2 MATHEMATICS Pub Date : 2023-03-04 DOI: 10.12775/tmna.2022.057
Dario Corona, R. Giambò, F. Giannoni, P. Piccione
In this paper %dedicated to the memory of Edward Fadell and Sufian Husseiniwe show how the notion of the Lusternik-Schnirelmann relative category can be usedto study a multiplicity problem for brake orbits in a potential wellwhich is homeomorphic to the $N$-dimensional unit disk.The estimate of the relative category of the set of chords with endpoints on the$(N-1)$-unit sphere was shown to the third author byFadell and Husseini while he was visiting the University of Wisconsin at Madison.
在本文中,Edward Fadell和Sufian Husseiniwe展示了Lusternik-Schnirelmann相对范畴的概念如何用于研究势阱中制动轨道的多重性问题,该势阱同胚于$N$维单位圆盘。Fadell和Husseini在第三作者访问威斯康星大学麦迪逊分校时向他展示了在$(N-1)$单位球面上具有端点的一组和弦的相对类别的估计。
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引用次数: 0
Reeb graphs of circle-valued functions: A survey and basic facts 圆值函数的Reeb图:综述与基本事实
IF 0.7 4区 数学 Q2 MATHEMATICS Pub Date : 2023-03-04 DOI: 10.12775/tmna.2022.023
Irina Gelbukh
The Reeb graph of a circle-valued function is a topological space obtained by contracting connected components of level sets (preimages of points) to points.For some smooth functions, the Reeb graph has the structure of a finite graph.This notion finds numerous applications in the theory of dynamical systems, as well as in the topological classification of circle-valued functions and the study of their homotopy properties.However, important theoretical facts on the topological properties of the Reeb graphs of circle-valued functions are scattered across numerous papers on different topics, according to the specific needs of the corresponding application.In this paper, we systematize the existing results on the Reeb graphs of circle-valued functions and generalize some of them to wider classes of functions or spaces.We also show how some results can be carried out from real-valued functions. Finally, we adapt some facts from the theory of foliations to the Reeb graphs of circle-valued functions.In particular, we analyze the cycle rank of the Reeb graph and address the problem of realization of a finite graph as a Reeb graph.
圆值函数的Reeb图是通过将水平集(点的前像)的连通分量收缩到点而获得的拓扑空间。对于一些光滑函数,Reeb图具有有限图的结构。这一概念在动力系统理论中,以及在圆值函数的拓扑分类和对其同伦性的研究中有许多应用。然而,根据相应应用的具体需要,关于圆值函数的Reeb图的拓扑性质的重要理论事实分散在不同主题的众多论文中。本文系统化了关于圆值函数的Reeb图的现有结果,并将其中的一些结果推广到更广泛的函数或空间类。我们还展示了如何从实值函数中得到一些结果。最后,我们将叶理理论中的一些事实应用于圆值函数的Reeb图。特别地,我们分析了Reeb图的循环秩,并解决了有限图作为Reeb图实现的问题。
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引用次数: 0
期刊
Topological Methods in Nonlinear Analysis
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