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Topological Methods in Nonlinear Analysis最新文献

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Fixed point indices and fixed words at infinity of selfmaps of graphs II 图的自映射的不动点指标和无穷远处的不动字
4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2023-02-26 DOI: 10.12775/tmna.2022.007
Qiang Zhang, Xuezhi Zhao
{"title":"Fixed point indices and fixed words at infinity of selfmaps of graphs II","authors":"Qiang Zhang, Xuezhi Zhao","doi":"10.12775/tmna.2022.007","DOIUrl":"https://doi.org/10.12775/tmna.2022.007","url":null,"abstract":"The index $mathrm{ind}(mathbf{F})$ of a fixed point class $mathbf{F}$ is a classical invariant in the Nielsen fixed point theory. In the recent paper cite{ZZ}, the authors introduced a new invariant $mathrm{ichr}(mathbf{F})$ called the improved characteristic, and proved that $mathrm{ind}(mathbf{F})leq mathrm{ichr}(mathbf{F})$ for all fixed point classes of $pi_1$-injective selfmaps of connected finite graphs. In this note, we show that the two homotopy invariants mentioned above are exactly the same. Since the improved characteristic is totally determined by the endomorphism of the fundamental group, we give a group-theoretical approach to compute indices of fixed point classes of graph selfmaps. As a consequence, we give a new criterion of a fixed point, which extends the one due to Gaboriau, Jaeger, Levitt and Lustig.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136042197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Realization of a graph as the Reeb graph of a height function on an embedded surface 在嵌入曲面上将图实现为高度函数的Reeb图
IF 0.7 4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2023-01-25 DOI: 10.12775/tmna.2021.058
Irina Gelbukh
{"title":"Realization of a graph as the Reeb graph of a height function on an embedded surface","authors":"Irina Gelbukh","doi":"10.12775/tmna.2021.058","DOIUrl":"https://doi.org/10.12775/tmna.2021.058","url":null,"abstract":"We show that for a given finite graph $G$ without loop edges and isolated vertices, there exists an embedding of a closed orientable surface in $mathbb{R}^3$\u0000such that the Reeb graph of the associated height function has the structure of $G$.\u0000In particular, this gives a positive answer to the corresponding question posed by Masumoto and Saeki in 2011.\u0000We also give a criterion for a given surface to admit such a realization of a given graph, and study the problem in the class of Morse functions\u0000and in the class of round Morse-Bott functions.\u0000In the case of realization up to homeomorphism, the height function can be chosen Morse-Bott;\u0000we estimate from below the number of its critical circles and the number of its isolated critical points in terms of the graph structure.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41267184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 solutions for the Brezis-Nirenberg problem 布雷齐斯-尼伦堡问题解的存在性
IF 0.7 4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2023-01-25 DOI: 10.12775/tmna.2022.029
Francisco Odair de Paiva, O. Miyagaki, Adilson E. Presoto
{"title":"Existence of solutions for the Brezis-Nirenberg problem","authors":"Francisco Odair de Paiva, O. Miyagaki, Adilson E. Presoto","doi":"10.12775/tmna.2022.029","DOIUrl":"https://doi.org/10.12775/tmna.2022.029","url":null,"abstract":"We are concerned with of existence of solutions to the semilinear elliptic problem\u0000$$\u0000 begin{cases}\u0000 - Delta u=lambda_{k}u+u^3 &text{in } Omega, \u0000 u= 0 &text{on }partial Omega,\u0000 end{cases}\u0000$$%\u0000in a bounded domain $Omega subset mathbb{R}^{4}$. Here $lambda_k$\u0000is an eigenvalue of the $-Delta$ in $H_0^1(Omega)$. We prove that this problem has a nontrivial solution.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43340171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Fourth-order elliptic problems involving concave-superlinear nonlinearities 涉及凹-超线性非线性的四阶椭圆问题
IF 0.7 4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2022-12-11 DOI: 10.12775/tmna.2022.011
T. Cavalcante, Edcarlos D. Silva
{"title":"Fourth-order elliptic problems involving concave-superlinear nonlinearities","authors":"T. Cavalcante, Edcarlos D. Silva","doi":"10.12775/tmna.2022.011","DOIUrl":"https://doi.org/10.12775/tmna.2022.011","url":null,"abstract":"The existence of solutions for a huge class of superlinear elliptic problems involving fourth-order elliptic problems defined on bounded domains\u0000under Navier boundary conditions is established. To this end we do not apply the well-known\u0000Ambrosetti-Rabinowitz condition. Instead, we assume that the nonlinear term\u0000is nonquadratic at infinity. Furthermore, the nonlinear term is a concave-superlinear function which can be indefinite in sign. \u0000In order to apply variational methods we employ some delicate arguments recovering some kind of compactness.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45984491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 3
On radial solutions for some elliptic equations involving operators with unbounded coefficients in exterior domains 一类外域无界系数算子椭圆型方程的径向解
IF 0.7 4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2022-12-11 DOI: 10.12775/tmna.2022.026
Anderson L. A. de Araujo, Luiz F. O. Faria, S. Alarcón, Leonelo Iturriaga
{"title":"On radial solutions for some elliptic equations involving operators with unbounded coefficients in exterior domains","authors":"Anderson L. A. de Araujo, Luiz F. O. Faria, S. Alarcón, Leonelo Iturriaga","doi":"10.12775/tmna.2022.026","DOIUrl":"https://doi.org/10.12775/tmna.2022.026","url":null,"abstract":"We study existence and multiplicity of radial solutions for some quasilinear elliptic\u0000 problems involving the operator $L_N=Delta - xcdot nabla$ on\u0000$mathbb{R}^Nsetminus B_1$, where $Delta$ is the Laplacian,\u0000 $xcdot nabla$ is an unbounded drift term, $Ngeq 3$ and $B_1$ is the unit ball centered at the origin.\u0000We consider: (i) Eigenvalue problems, and (ii) Problems involving a nonlinearity of concave and convex type. On the first class of problems we get a compact\u0000 embedding result, whereas on the second, we address the well-known question\u0000of Ambrosetti, Brezis and Cerami from 1993 concerning the existence of two positive\u0000 solutions for some problems involving the supercritical Sobolev exponent in symmetric domains for the Laplacian. Specifically, we providelinebreak a new approach of\u0000 answering the ABC-question for elliptic problems with unbounded coefficients in\u0000 exterior domains and we find asymptotic properties of the radial solutions. Furthermore, we study the limit case, namely when nonlinearity involves\u0000a sublinear term and a linear term. As far as we know, this is the first work that deals with such a case, even for the Laplacian. In our approach,\u0000 we use both topological and variational arguments.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47651785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
An accelerated variant of the projection based parallel hybrid algorithm for split null point problems 求解分裂零点问题的基于投影的并行混合算法的一种加速变体
IF 0.7 4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2022-12-10 DOI: 10.12775/tmna.2022.015
Yasir Arfat, P. Kumam, M. A. A. Khan, P. S. Ngiamsunthorn
{"title":"An accelerated variant of the projection based parallel hybrid algorithm for split null point problems","authors":"Yasir Arfat, P. Kumam, M. A. A. Khan, P. S. Ngiamsunthorn","doi":"10.12775/tmna.2022.015","DOIUrl":"https://doi.org/10.12775/tmna.2022.015","url":null,"abstract":"In this paper, we consider an accelerated shrinking projection based parallel hybrid algorithm to study the split null point problem (SNPP) associated with the maximal monotone operators in Hilbert spaces. The analysis of the proposed algorithm provides strong convergence results under suitable set of control conditions as well as viability with the help of a numerical experiment. The results presented in this paper improve various existing results in the current literature.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44746966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 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
Topological Methods in Nonlinear Analysis Pub Date : 2022-12-10 DOI: 10.12775/tmna.2022.009
Yansheng Shen, Xumin Wang
{"title":"Existence results for fractional Brezis-Nirenberg type problems in unbounded domains","authors":"Yansheng Shen, Xumin Wang","doi":"10.12775/tmna.2022.009","DOIUrl":"https://doi.org/10.12775/tmna.2022.009","url":null,"abstract":"In this paper we study the fractional Brezis-Nirenberg type problems in unbounded cylinder-type domains\u0000begin{align*}\u0000begin{cases}\u0000(-Delta)^{s}u-mudfrac{u}{|x|^{2s}}=lambda u+|u|^{2^{ast}_{s}-2}u\u0000 & text{in } Omega,\u0000 u=0 & text{in } mathbb{R}^{N}setminus Omega,\u0000end{cases}\u0000end{align*}\u0000where $(-Delta)^{s}$ is the fractional Laplace operator with $sin(0,1)$,\u0000$muin[0,Lambda_{N,s})$ with $Lambda_{N,s}$ the best fractional Hardy constant, $lambda> 0$, $N> 2s$ and $2^{ast}_{s}={2N}/({N-2s})$\u0000denotes the fractional critical Sobolev exponent. By applying the fractional\u0000Poincaré inequality together with the concentration-compactness principle\u0000for fractional Sobolev spaces in unbounded domains, we prove an existence\u0000result to the equation.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42168030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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
Topological Methods in Nonlinear Analysis Pub Date : 2022-12-10 DOI: 10.12775/tmna.2022.022
Xinyu Mei, T. Sun, Yongqin Xie, Kaixuan Zhu
{"title":"Time-dependent global attractors for the strongly damped wave equations with lower regular forcing term","authors":"Xinyu Mei, T. Sun, Yongqin Xie, Kaixuan Zhu","doi":"10.12775/tmna.2022.022","DOIUrl":"https://doi.org/10.12775/tmna.2022.022","url":null,"abstract":"In this paper, based on a new theoretical framework of\u0000time-dependent global attractors (Conti, Pata and Temam cite{CPT13}),\u0000we consider the strongly damped wave equations $varepsilon(t)u_{tt}-Delta u_{t}-Delta u+f(u)=g(x)$\u0000and establish the existence of attractors\u0000in $mathcal{H}_{t}=H_{0}^{1}(Omega)times L^{2}(Omega)$\u0000and $mathcal{V}_{t}=H_{0}^{1}(Omega)times H_{0}^{1}(Omega)$, respectively.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42920835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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
Topological Methods in Nonlinear Analysis Pub Date : 2022-12-10 DOI: 10.12775/tmna.2022.013
M. Batista, José I. Santos
{"title":"A note on local minimizers of energy on complete manifolds","authors":"M. Batista, José I. Santos","doi":"10.12775/tmna.2022.013","DOIUrl":"https://doi.org/10.12775/tmna.2022.013","url":null,"abstract":"In this paper, we study the geometric rigidity of complete Riemannian manifolds admitting local minimizers of energy functionals.\u0000More precisely, assuming the existence of a non-trivial local minimizer and under suitable assumptions, a Riemannian manifold under consideration must be\u0000a product manifold furnished with a warped metric.\u0000Secondly, under similar hypotheses, we deduce a geometrical splitting in\u0000the same fashion as in the Cheeger-Gromoll splitting theorem and we also get information about local minimizers.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41321676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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
Topological Methods in Nonlinear Analysis Pub Date : 2022-12-10 DOI: 10.12775/tmna.2022.016
Zhenping Feng, Zhuoran Du
{"title":"Periodic solutions of fractional Laplace equations: Least period, axial symmetry and limit","authors":"Zhenping Feng, Zhuoran Du","doi":"10.12775/tmna.2022.016","DOIUrl":"https://doi.org/10.12775/tmna.2022.016","url":null,"abstract":"We are concerned with periodic solutions of the fractional Laplace equation\u0000begin{equation*}\u0000{(-partial_{xx})^s}u(x)+F'(u(x))=0 quad mbox{in }mathbb{R},\u0000end{equation*}\u0000where $0< s< 1$. The smooth function $F$ is a double-well potential with wells at\u0000$+1$ and $-1$. We show that the value of least positive period is\u0000$2{pi}times({1}/{-F''(0)})^{{1}/({2s})}$.\u0000 The axial symmetry of odd periodic solutions is obtained by moving plane method.\u0000We also prove that odd periodic solutions $u_{T}(x)$ converge to a layer solution\u0000 of the same equation as periods $Trightarrow+infty$.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44242890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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