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Existence of positive solutions for Kirchhoff-type problem in exterior domains Kirchhoff型问题外域正解的存在性
IF 0.7 3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2023-02-01 DOI: 10.1017/S001309152300010X
Liqian Jia, Xinfu Li, Shiwang Ma
{"title":"Existence of positive solutions for Kirchhoff-type problem in exterior domains","authors":"Liqian Jia, Xinfu Li, Shiwang Ma","doi":"10.1017/S001309152300010X","DOIUrl":"https://doi.org/10.1017/S001309152300010X","url":null,"abstract":"Abstract We consider the following Kirchhoff-type problem in an unbounded exterior domain $Omegasubsetmathbb{R}^{3}$: (*)\u0000begin{align}\u0000left{\u0000begin{array}{ll}\u0000-left(a+bdisplaystyle{int}_{Omega}|nabla u|^{2},{rm d}xright)triangle u+lambda u=f(u), & xinOmega,\u0000\u0000u=0, & xinpartial Omega,\u0000end{array}right.\u0000end{align}where a > 0, $bgeq0$, and λ > 0 are constants, $partialOmeganeqemptyset$, $mathbb{R}^{3}backslashOmega$ is bounded, $uin H_{0}^{1}(Omega)$, and $fin C^1(mathbb{R},mathbb{R})$ is subcritical and superlinear near infinity. Under some mild conditions, we prove that if begin{equation*}-Delta u+lambda u=f(u), qquad xin mathbb R^3 end{equation*}has only finite number of positive solutions in $H^1(mathbb R^3)$ and the diameter of the hole $mathbb R^3setminus Omega$ is small enough, then the problem (*) admits a positive solution. Same conclusion holds true if Ω is fixed and λ > 0 is small. To our best knowledge, there is no similar result published in the literature concerning the existence of positive solutions to the above Kirchhoff equation in exterior domains.","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"66 1","pages":"182 - 217"},"PeriodicalIF":0.7,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44214441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Free rank of symmetry of products of Dold manifolds 多德流形积对称的自由秩
IF 0.7 3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2023-02-01 DOI: 10.1017/S0013091523000068
Pinka Dey
{"title":"Free rank of symmetry of products of Dold manifolds","authors":"Pinka Dey","doi":"10.1017/S0013091523000068","DOIUrl":"https://doi.org/10.1017/S0013091523000068","url":null,"abstract":"Abstract Dold manifolds $P(m,n)$ are certain twisted complex projective space bundles over real projective spaces and serve as generators for the unoriented cobordism algebra of smooth manifolds. The paper investigates the structure of finite groups that act freely on products of Dold manifolds. It is proved that if a finite group G acts freely and $ mathbb{Z}_2 $ cohomologically trivially on a finite CW-complex homotopy equivalent to ${prod_{i=1}^{k} P(2m_i,n_i)}$, then $Gcong (mathbb{Z}_2)^l$ for some $lleq k$ (see Theorem A for the exact bound). We also determine some bounds in the case when for each i, ni is even and mi is arbitrary. As a consequence, the free rank of symmetry of these manifolds is determined for cohomologically trivial actions.","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"66 1","pages":"117 - 132"},"PeriodicalIF":0.7,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46883159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Synchronization of coupled map lattices 耦合映射格的同步
IF 0.7 3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2023-02-01 DOI: 10.1017/S0013091523000081
A. Baraviera, P. Duarte, M. J. Torres
{"title":"Synchronization of coupled map lattices","authors":"A. Baraviera, P. Duarte, M. J. Torres","doi":"10.1017/S0013091523000081","DOIUrl":"https://doi.org/10.1017/S0013091523000081","url":null,"abstract":"Abstract In this paper, we address the issue of synchronization of coupled systems, introducing concepts of local and global synchronization for a class of systems that extend the model of coupled map lattices. A criterion for local synchronization is given; numerical experiments are exhibited to illustrate the criteria and also to raise some questions in the end of the text.","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"66 1","pages":"143 - 163"},"PeriodicalIF":0.7,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56897207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Common index divisor of the number fields defined by $x^5+,ax,+b$ $x^5+，ax，+b定义的数字域的公共索引除数$
IF 0.7 3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2022-11-01 DOI: 10.1017/S0013091522000529
Anuj Jakhar, Sumandeep Kaur, Surender Kumar
{"title":"Common index divisor of the number fields defined by $x^5+,ax,+b$","authors":"Anuj Jakhar, Sumandeep Kaur, Surender Kumar","doi":"10.1017/S0013091522000529","DOIUrl":"https://doi.org/10.1017/S0013091522000529","url":null,"abstract":"Abstract Let $K={mathbf {Q}}(theta )$ be an algebraic number field with $theta$ a root of an irreducible polynomial $x^5+ax+bin {mathbf {Z}}[x]$. In this paper, for every rational prime $p$, we provide necessary and sufficient conditions on $a,,~b$ so that $p$ is a common index divisor of $K$. In particular, we give sufficient conditions on $a,,~b$ for which $K$ is non-monogenic. We illustrate our results through examples.","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"65 1","pages":"1147 - 1161"},"PeriodicalIF":0.7,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43563895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
PEM series 2 volume 65 issue 4 Cover and Back matter PEM系列2第65卷第4期封面和封底
IF 0.7 3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2022-11-01 DOI: 10.1017/s0013091523000020
{"title":"PEM series 2 volume 65 issue 4 Cover and Back matter","authors":"","doi":"10.1017/s0013091523000020","DOIUrl":"https://doi.org/10.1017/s0013091523000020","url":null,"abstract":"","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":" ","pages":"b1 - b2"},"PeriodicalIF":0.7,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44934371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Conjugacy conditions for supersoluble complements of an abelian base and a fixed point result for non-coprime actions 阿贝尔基超可解补的共轭条件和非互质作用的不动点结果
IF 0.7 3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2022-11-01 DOI: 10.1017/S0013091522000499
Michael C. Burkhart
{"title":"Conjugacy conditions for supersoluble complements of an abelian base and a fixed point result for non-coprime actions","authors":"Michael C. Burkhart","doi":"10.1017/S0013091522000499","DOIUrl":"https://doi.org/10.1017/S0013091522000499","url":null,"abstract":"Abstract We demonstrate that two supersoluble complements of an abelian base in a finite split extension are conjugate if and only if, for each prime $p$, a Sylow $p$-subgroup of one complement is conjugate to a Sylow $p$-subgroup of the other. As a corollary, we find that any two supersoluble complements of an abelian subgroup $N$ in a finite split extension $G$ are conjugate if and only if, for each prime $p$, there exists a Sylow $p$-subgroup $S$ of $G$ such that any two complements of $Scap N$ in $S$ are conjugate in $G$. In particular, restricting to supersoluble groups allows us to ease D. G. Higman's stipulation that the complements of $Scap N$ in $S$ be conjugate within $S$. We then consider group actions and obtain a fixed point result for non-coprime actions analogous to Glauberman's lemma.","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"65 1","pages":"1075 - 1079"},"PeriodicalIF":0.7,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46109688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Dirichlet vs Neumann 狄利克雷和诺伊曼
IF 0.7 3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2022-11-01 DOI: 10.1017/S0013091522000487
E. Marušić‐Paloka
{"title":"Dirichlet vs Neumann","authors":"E. Marušić‐Paloka","doi":"10.1017/S0013091522000487","DOIUrl":"https://doi.org/10.1017/S0013091522000487","url":null,"abstract":"Abstract We study the asymptotic behaviour of the periodically mixed Zaremba problem. We cover the part of the boundary by a chess board with a small period (square size) $varepsilon$ and impose the Dirichlet condition on black and the Neumann condition on white squares. As $varepsilon to 0$, we get the effective boundary condition which is always of the Dirichlet type. The Dirichlet data on the boundary, however, depend on the ratio between the magnitudes of the two boundary values.","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"65 1","pages":"1063 - 1074"},"PeriodicalIF":0.7,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42846585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
FP-injective dimensions and Gorenstein homology fp -内射维数与Gorenstein同调
IF 0.7 3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2022-11-01 DOI: 10.1017/S0013091522000542
Gang Yang, Junpeng Wang
{"title":"FP-injective dimensions and Gorenstein homology","authors":"Gang Yang, Junpeng Wang","doi":"10.1017/S0013091522000542","DOIUrl":"https://doi.org/10.1017/S0013091522000542","url":null,"abstract":"Abstract Let $R$ be a left coherent ring. It is proven that if an $R$-module $M$ has a finite FP-injective dimension, then the Gorenstein projective (resp. Gorenstein flat) dimension and the projective (resp. flat) dimension coincide. Also, we obtain that the pair ($mathcal {GP},, mathcal {GP}^{perp }$) forms a projective cotorsion pair under some mild conditions.","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"65 1","pages":"1183 - 1199"},"PeriodicalIF":0.7,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49102083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
PEM series 2 volume 65 issue 4 Cover and Front matter PEM系列2卷65期4封面和封面问题
IF 0.7 3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2022-11-01 DOI: 10.1017/s0013091523000019
{"title":"PEM series 2 volume 65 issue 4 Cover and Front matter","authors":"","doi":"10.1017/s0013091523000019","DOIUrl":"https://doi.org/10.1017/s0013091523000019","url":null,"abstract":"","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":" ","pages":"f1 - f2"},"PeriodicalIF":0.7,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48560278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Elliptic equation with van der Waals type potential 范德华势椭圆方程
IF 0.7 3区 数学
Proceedings of the Edinburgh Mathematical Society Pub Date : 2022-10-18 DOI: 10.1017/S0013091522000451
Yujian Su, Senli Liu
{"title":"Elliptic equation with van der Waals type potential","authors":"Yujian Su, Senli Liu","doi":"10.1017/S0013091522000451","DOIUrl":"https://doi.org/10.1017/S0013091522000451","url":null,"abstract":"Abstract In this paper, we study the Lieb's translation lemma in Coulomb–Sobolev space and then apply it to investigate the existence of Pohožaev type ground state solution for elliptic equation with van der Waals type potential.","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"65 1","pages":"1048 - 1062"},"PeriodicalIF":0.7,"publicationDate":"2022-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44568211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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