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Journal of Fixed Point Theory and Applications最新文献

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Stability of the braid types defined by the symplecticmorphisms preserving a link 保留链接的交映变形所定义的辫状类型的稳定性
IF 1.8 3区 数学
Journal of Fixed Point Theory and Applications Pub Date : 2024-02-13 DOI: 10.1007/s11784-023-01095-3
{"title":"Stability of the braid types defined by the symplecticmorphisms preserving a link","authors":"","doi":"10.1007/s11784-023-01095-3","DOIUrl":"https://doi.org/10.1007/s11784-023-01095-3","url":null,"abstract":"<h3>Abstract</h3> <p>Fix a suitable link on the disk. Recently, F. Morabito associates each Hamiltonian symplecticmorphism preserving the link to a braid type. Based on this construction, Morabito defines a family of pseudometrics on the braid groups by using the Hofer metric. In this paper, we show that two Hamiltonian symplecticmorphisms define the same braid type provided that their Hofer distance is sufficiently small. As a corollary, the pseudometrics defined by Morabito are nondegenerate.</p>","PeriodicalId":54835,"journal":{"name":"Journal of Fixed Point Theory and Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139759079","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
Multiple ordered solutions for a class of quasilinear problem with oscillating nonlinearity 一类具有振荡非线性的准线性问题的多重有序解
IF 1.8 3区 数学
Journal of Fixed Point Theory and Applications Pub Date : 2024-02-13 DOI: 10.1007/s11784-023-01096-2
Gelson C. G. dos Santos, Julio Roberto S. Silva
{"title":"Multiple ordered solutions for a class of quasilinear problem with oscillating nonlinearity","authors":"Gelson C. G. dos Santos, Julio Roberto S. Silva","doi":"10.1007/s11784-023-01096-2","DOIUrl":"https://doi.org/10.1007/s11784-023-01096-2","url":null,"abstract":"<p>In this paper, we use truncation argument combined with method of minimization, argument of comparison, topological degree arguments and sub-supersolutions method to show existence of multiple positive solutions (which are ordered in the <span>(C(overline{Omega }))</span>-norm) for the following class of problems: </p><span>$$begin{aligned} left{ begin{aligned} -&amp;Delta u - kappa Delta (u^{2}) u +mu |u|^{q-2}u = lambda f(u)+h(u) text{ in } Omega , u&amp;=0 text{ on } partial Omega , end{aligned} right. end{aligned}$$</span><p>where <span>(Omega )</span> is a bounded smooth domain of <span>(mathbb {R}^N)</span> <span>((Nge 1), kappa ,mu ,lambda &gt; 0,qge 1)</span> are parameters, the nonlinearity <span>(f: mathbb {R}rightarrow mathbb {R})</span> is a continuous function that can change sign and satisfies an area condition and <span>(h: mathbb {R}rightarrow mathbb {R})</span> is a general nonlinearity.</p>","PeriodicalId":54835,"journal":{"name":"Journal of Fixed Point Theory and Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139759332","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
Vũ Ngọc’s conjecture on focus-focus singular fibers with multiple pinched points Vũ Ngọn phương đúng (吴冠中)关于多夹点聚焦奇异纤维的猜想
IF 1.8 3区 数学
Journal of Fixed Point Theory and Applications Pub Date : 2024-01-25 DOI: 10.1007/s11784-023-01089-1
Álvaro Pelayo, Xiudi Tang
{"title":"Vũ Ngọc’s conjecture on focus-focus singular fibers with multiple pinched points","authors":"Álvaro Pelayo, Xiudi Tang","doi":"10.1007/s11784-023-01089-1","DOIUrl":"https://doi.org/10.1007/s11784-023-01089-1","url":null,"abstract":"<p>We classify, up to fiberwise symplectomorphisms, a saturated neighborhood of a singular fiber of an integrable system (which is proper onto its image and has connected fibers) containing <span>(k geqslant 1)</span> focus-focus critical points. Our proof recovers the classification for <span>(k=1)</span> which was known prior to this paper. Our result shows that there is a one-to-one correspondence between such neighborhoods and <i>k</i> formal power series, up to a <span>((mathbb {Z}_2 times D_k))</span>-action, where <span>(D_k)</span> is the <i>k</i>th dihedral group. The <i>k</i> formal power series determine the dynamical behavior of the Hamiltonian vector fields associated to the components of the momentum map on the symplectic manifold <span>((M,omega ))</span> near the singular fiber containing the <i>k</i> focus-focus critical points. This proves a conjecture of San Vũ Ngọc from 2003.</p>","PeriodicalId":54835,"journal":{"name":"Journal of Fixed Point Theory and Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139581203","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
Transverse foliations in the rotating Kepler problem 旋转开普勒问题中的横切面
IF 1.8 3区 数学
Journal of Fixed Point Theory and Applications Pub Date : 2024-01-19 DOI: 10.1007/s11784-023-01090-8
Seongchan Kim
{"title":"Transverse foliations in the rotating Kepler problem","authors":"Seongchan Kim","doi":"10.1007/s11784-023-01090-8","DOIUrl":"https://doi.org/10.1007/s11784-023-01090-8","url":null,"abstract":"<p>We construct finite energy foliations and transverse foliations of neighbourhoods of the circular orbits in the rotating Kepler problem for all negative energies. This paper would be a first step towards our ultimate goal that is to recover and refine McGehee’s results on homoclinics [23] and to establish a theoretical foundation to the numerical demonstration of the existence of a homoclinic–heteroclinic chain in the planar circular restricted three-body problem [20], using pseudoholomorphic curves.</p>","PeriodicalId":54835,"journal":{"name":"Journal of Fixed Point Theory and Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139508335","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
Simple closed geodesics in dimensions $$ge 3$$ 尺寸为 $$ge 3$$ 的简单闭合大地线
IF 1.8 3区 数学
Journal of Fixed Point Theory and Applications Pub Date : 2024-01-19 DOI: 10.1007/s11784-023-01092-6
{"title":"Simple closed geodesics in dimensions $$ge 3$$","authors":"","doi":"10.1007/s11784-023-01092-6","DOIUrl":"https://doi.org/10.1007/s11784-023-01092-6","url":null,"abstract":"<h3>Abstract</h3> <p>We show that for a generic Riemannian or reversible Finsler metric on a compact differentiable manifold <em>M</em> of dimension at least three all closed geodesics are simple and do not intersect each other. Using results by Contreras (Ann Math 2(172):761–808, 2010; in: Proceedings of International Congress Mathematicians (ICM 2010) Hyderabad, India, pp 1729–1739, 2011) this shows that for a generic Riemannian metric on a compact and simply-connected manifold all closed geodesics are simple and the number <em>N</em>(<em>t</em>) of geometrically distinct closed geodesics of length <span> <span>(le t)</span> </span> grows exponentially.</p>","PeriodicalId":54835,"journal":{"name":"Journal of Fixed Point Theory and Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139508315","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
Cuplength estimates for time-periodic measures of Hamiltonian systems with diffusion 有扩散的哈密尔顿系统的时间周期测量的杯长估计
IF 1.8 3区 数学
Journal of Fixed Point Theory and Applications Pub Date : 2024-01-10 DOI: 10.1007/s11784-023-01093-5
Oliver Fabert
{"title":"Cuplength estimates for time-periodic measures of Hamiltonian systems with diffusion","authors":"Oliver Fabert","doi":"10.1007/s11784-023-01093-5","DOIUrl":"https://doi.org/10.1007/s11784-023-01093-5","url":null,"abstract":"<p>We show how methods from Hamiltonian Floer theory can be used to establish lower bounds for the number of different time-periodic measures of time-periodic Hamiltonian systems with diffusion. After proving the existence of closed random periodic solutions and of the corresponding Floer curves for Hamiltonian systems with random walks with step width 1/<i>n</i> for every <span>(nin mathbb {N})</span>, we show that, after passing to a subsequence, they converge in probability distribution as <span>(nrightarrow infty )</span>. Besides using standard results from Hamiltonian Floer theory and about convergence of tame probability measures, we crucially use that sample paths of Brownian motion are almost surely Hölder continuous with Hölder exponent <span>(0&lt;alpha &lt;frac{1}{2})</span>.</p>","PeriodicalId":54835,"journal":{"name":"Journal of Fixed Point Theory and Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139413375","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
Correction to: Conley index theory without index pairs. I: The point-set level theory 更正：无指数对的康利指数理论。I:点集水平理论
IF 1.8 3区 数学
Journal of Fixed Point Theory and Applications Pub Date : 2023-12-28 DOI: 10.1007/s11784-023-01094-4
Yosuke Morita
{"title":"Correction to: Conley index theory without index pairs. I: The point-set level theory","authors":"Yosuke Morita","doi":"10.1007/s11784-023-01094-4","DOIUrl":"https://doi.org/10.1007/s11784-023-01094-4","url":null,"abstract":"","PeriodicalId":54835,"journal":{"name":"Journal of Fixed Point Theory and Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139152960","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
Correction to: L∞(Ω)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$L^infty (Omega )$$end{document} a priori estima 更正为L∞(Ω)documentclass[12pt]{minimal}usepackage{amsmath}usepackage{wasysym}usepackage{amsfonts} （我们的软件包{amsfonts}）。usepackage{amssymb} （我们的软件包{amssymb}）。usepackage{amsbsy} usepackage{mathrsfs}usepackage{upgreek} （上希腊语setlengthoddsidemargin}{-69pt} （长度设置{-69pt}）。begin{document}$$L^infty (Omega )$$end{document} a priori estima
IF 1.8 3区 数学
Journal of Fixed Point Theory and Applications Pub Date : 2023-12-10 DOI: 10.1007/s11784-023-01091-7
R. Pardo
{"title":"Correction to: L∞(Ω)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$L^infty (Omega )$$end{document} a priori estima","authors":"R. Pardo","doi":"10.1007/s11784-023-01091-7","DOIUrl":"https://doi.org/10.1007/s11784-023-01091-7","url":null,"abstract":"","PeriodicalId":54835,"journal":{"name":"Journal of Fixed Point Theory and Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138585212","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
Existence of non-radial solutions to semilinear elliptic systems on a unit ball in $${mathbb {R}}^3$$ 单位球上半线性椭圆系统非径向解的存在性 $${mathbb {R}}^3$$
IF 1.8 3区 数学
Journal of Fixed Point Theory and Applications Pub Date : 2023-11-20 DOI: 10.1007/s11784-023-01086-4
Jingzhou Liu, Carlos García-Azpeitia, Wieslaw Krawcewicz
{"title":"Existence of non-radial solutions to semilinear elliptic systems on a unit ball in $${mathbb {R}}^3$$","authors":"Jingzhou Liu, Carlos García-Azpeitia, Wieslaw Krawcewicz","doi":"10.1007/s11784-023-01086-4","DOIUrl":"https://doi.org/10.1007/s11784-023-01086-4","url":null,"abstract":"<p>In this paper, we prove the existence of non-radial solutions to the problem <span>(-triangle u= f(x,u))</span>, <span>(u|_{partial Omega }=0)</span> on the unit ball <span>(Omega :={xin {mathbb {R}}^3: Vert xVert &lt;1})</span> with <span>(u(x)in {mathbb {R}}^s)</span>, where <i>f</i> is a sub-linear continuous function, differentiable with respect to <i>u</i> at zero and satisfying <span>(f(gx,u) = f(x,u))</span> for all <span>(gin O(3))</span>, <span>( f(x,-u)=- f(x,u))</span>. We investigate symmetric properties of the corresponding non-radial solutions. The abstract result is supported by a numerical example.</p>","PeriodicalId":54835,"journal":{"name":"Journal of Fixed Point Theory and Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138516169","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
Slicing the Nash equilibrium manifold 切纳什均衡流形
3区 数学
Journal of Fixed Point Theory and Applications Pub Date : 2023-11-13 DOI: 10.1007/s11784-023-01088-2
Yehuda John Levy
{"title":"Slicing the Nash equilibrium manifold","authors":"Yehuda John Levy","doi":"10.1007/s11784-023-01088-2","DOIUrl":"https://doi.org/10.1007/s11784-023-01088-2","url":null,"abstract":"Abstract This paper uses tools on the structure of the Nash equilibrium correspondence of strategic-form games to characterize a class of fixed-point correspondences, that is, correspondences assigning, for a given parametrized function, the fixed-points associated with each value of the parameter. After generalizing recent results from the game-theoretic literature, we deduce that every fixed-point correspondence associated with a semi-algebraic function is the projection of a Nash equilibrium correspondence, and hence its graph is a slice of a projection, as well as a projection of a slice, of a manifold that is homeomorphic, even isotopic, to a Euclidean space. As a result, we derive an illustrative proof of Browder’s theorem for fixed-point correspondences.","PeriodicalId":54835,"journal":{"name":"Journal of Fixed Point Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136283098","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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