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Topological Methods in Nonlinear Analysis最新文献

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Multiple normalized solutions for a quasi-linear Schrödinger equation via dual approach 拟线性Schrödinger方程的多重归一化对偶解
IF 0.7 4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2023-02-26 DOI: 10.12775/tmna.2022.052
Lin Zhang, Yongqing Li, Zhi-Qiang Wang
{"title":"Multiple normalized solutions for a quasi-linear Schrödinger equation via dual approach","authors":"Lin Zhang, Yongqing Li, Zhi-Qiang Wang","doi":"10.12775/tmna.2022.052","DOIUrl":"https://doi.org/10.12775/tmna.2022.052","url":null,"abstract":"In this paper, we construct multiple normalized solutions of the following from quasi-linear Schrödinger equation:\u0000\u0000-Delta u-Delta(|u|^{2})u-mu u=|u|^{p-2}u, quadtext{in } mathbb{R}^N,\u0000\u0000subject to a mass-subcritical constraint. In order to overcome non-smoothness of the associated variational formulation we make use of the dual approach.\u0000The constructed solutions possess energies being clustered at $0$ level which makes it difficult to use existing methods \u0000for non-smooth variational problems such as the variational perturbation approach.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41422826","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
The Wecken problem for coincidences of boundary preserving surface maps 保边界曲面图一致性的威肯问题
IF 0.7 4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2023-02-26 DOI: 10.12775/tmna.2022.061
M. R. Kelly
{"title":"The Wecken problem for coincidences of boundary preserving surface maps","authors":"M. R. Kelly","doi":"10.12775/tmna.2022.061","DOIUrl":"https://doi.org/10.12775/tmna.2022.061","url":null,"abstract":"We prove a Brooks type coincidence minimization result for boundary preserving maps on compact surfaces with boundary. \u0000 As an application we obtain non-boundary Wecken results for pairs of maps \u0000 $f,gcolon (X,partial X) to (X,partial X)$ for most surfaces $X$.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42674431","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
Bifurcation of solutions of $U(1)$-equivariant semilinear boundary value problems U(1)$-等变半线性边值问题解的分岔
IF 0.7 4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2023-02-26 DOI: 10.12775/tmna.2022.056
J. Pejsachowicz
{"title":"Bifurcation of solutions of $U(1)$-equivariant semilinear boundary value problems","authors":"J. Pejsachowicz","doi":"10.12775/tmna.2022.056","DOIUrl":"https://doi.org/10.12775/tmna.2022.056","url":null,"abstract":"Assuming that there is a known (trivial) branch of solutions of a parameterized family\u0000of equations, topological bifurcation studies the topological invariants of the linearized equations along the trivial branch whose nonvanishing entails the\u0000appearance of bifurcation from the trivial branch. We introduce here some refined topological invariants for semilinear elliptic boundary value problems equivariant\u0000with respect to the action of the circle $U(1)$ allowing to improve, in this case, \u0000some previously obtained bifurcation criteria for general nonlinear elliptic boundary value problems.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42997016","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
Lift factors for the Nielsen root theory on $n$-valued maps $n$值映射上Nielsen根理论的提升因子
IF 0.7 4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2023-02-26 DOI: 10.12775/tmna.2022.017
RobertF Brown, D. Gonçalves
{"title":"Lift factors for the Nielsen root theory on $n$-valued maps","authors":"RobertF Brown, D. Gonçalves","doi":"10.12775/tmna.2022.017","DOIUrl":"https://doi.org/10.12775/tmna.2022.017","url":null,"abstract":"A root of an $n$-valued map $varphi colon X to D_n(Y)$ at $a in Y$\u0000 is a point $x in X$ such that $a in varphi(x)$. We lift the map \u0000$varphi$ to a split $n$-valued map of finite covering spaces and\u0000 its single-valued factors are defined to be the lift factors of \u0000$varphi$. We describe the relationship between the root classes at $a$ \u0000of the lift factors and those of $varphi$. We define the \u0000Reidemeister root number $RR (varphi)$ in terms \u0000of the Reidemeister root numbers of the lift factors. We prove that the\u0000 Reidemeister root number is a homotopy invariant upper bound for \u0000the Nielsen root number $NR(varphi)$, the number of essential root classes,\u0000and we characterize essentiality by means of an \u0000equivalence relation called the $Phi$-relation. A theorem of Brooks states that \u0000a single-valued map to a closed connected manifold is root-uniform, that is,\u0000 its root classes are either all essential or all inessential. It \u0000follows that if $Y$ is a closed connected manifold, then the lift factors are \u0000root-uniform and we relate this property to the root-uniformity of $varphi$. \u0000 If $X$ and $Y$ are closed connected oriented manifolds of the same dimension then, by means of the lift factors, we define an integer-valued \u0000index of a root class of $varphi$ that is invariant under $Phi$-relation and this \u0000implies that if its index is non-zero, then the root class is essential.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49352063","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
$Z_2^k$-actions with connected fixed point set $Z_2^k$-具有连通不动点集的动作
IF 0.7 4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2023-02-26 DOI: 10.12775/tmna.2022.048
J. C. Costa, P. Pergher, Renato M. Moraes
{"title":"$Z_2^k$-actions with connected fixed point set","authors":"J. C. Costa, P. Pergher, Renato M. Moraes","doi":"10.12775/tmna.2022.048","DOIUrl":"https://doi.org/10.12775/tmna.2022.048","url":null,"abstract":"In this paper we describe the equivariant cobordism classification of smooth actions $(M^m,phi)$ of the group $G=mathbb{Z}_2^k$ on closed smooth\u0000$m$-dimensional manifolds $M^m$, for which the fixed point set of the action is a connected manifold of dimension n and $2^k n - 2^{k-1} leq m < 2^k n$.\u0000Here, $mathbb{Z}_2^k$ is considered as the group generated by $k$ commuting smooth involutions defined on $M^m$. \u0000This generalizes a previous result of 2008 of the second author, who obtained this type of classification for $k=2$ and $m=4n-1$ or $m=4n-2$.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42770974","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
$alpha$-$(h,e)$-convex operators and applications for Riemann-Liouville fractional differential equations $alpha$-$（h，e）$-凸算子及其在Riemann-Liouville分数阶微分方程中的应用
IF 0.7 4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2023-02-26 DOI: 10.12775/tmna.2022.014
Bibo Zhou, Lingling Zhang
{"title":"$alpha$-$(h,e)$-convex operators and applications for Riemann-Liouville fractional differential equations","authors":"Bibo Zhou, Lingling Zhang","doi":"10.12775/tmna.2022.014","DOIUrl":"https://doi.org/10.12775/tmna.2022.014","url":null,"abstract":"In this paper, we consider a class of $alpha$-$(h,e)$-convex operators defined\u0000 in set $P_{h,e}$ and applications with $alpha> 1$. Without assuming the operator\u0000to be completely continuous or compact, by employing cone theory and monotone\u0000 iterative technique, we not only obtain the existence and uniqueness of fixed point\u0000of $alpha$-$(h,e)$-convex operators, but also construct two monotone iterative\u0000 sequences to approximate the unique fixed point. At last, we investigate the\u0000 existence-uniqueness of a nontrivial solution for Riemann-Liouville fractional differential equations integral boundary value problems by employing\u0000$alpha$-$(h,e)$-convex operators fixed point theorem.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45209777","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
Periodic points of self-maps of products of lens spaces $L(3)times L(3)$ 透镜空间积L(3)乘以L(3)$的自映射的周期点
IF 0.7 4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2023-02-26 DOI: 10.12775/tmna.2022.053
J. Jezierski
{"title":"Periodic points of self-maps of products of lens spaces $L(3)times L(3)$","authors":"J. Jezierski","doi":"10.12775/tmna.2022.053","DOIUrl":"https://doi.org/10.12775/tmna.2022.053","url":null,"abstract":"Let $fcolon Mto M$ be a self-map of a compact manifold and $nin mathbb{N}$.\u0000The least number of $n$-periodic points in the smooth homotopy class of $f$ may be smaller than in the continuous homotopy class. We ask: for which self-maps\u0000$fcolon Mto M$ the two minima are the same, for each prescribed multiplicity?\u0000 In the study of self-maps of tori and compact Lie groups a necessary condition appears.\u0000Here we give a criterion which helps to decide whether the necessary condition is also sufficient.\u0000We apply this result to show that for self-maps of the product of the lens space $M=L(3)times L(3)$ the necessary condition is also sufficient.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46267926","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
Multiple solutions for perturbed quasilinear elliptic problems 扰动拟线性椭圆型问题的多重解
IF 0.7 4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2023-02-26 DOI: 10.12775/tmna.2022.069
R. Bartolo, A. M. Candela, A. Salvatore
{"title":"Multiple solutions for perturbed quasilinear elliptic problems","authors":"R. Bartolo, A. M. Candela, A. Salvatore","doi":"10.12775/tmna.2022.069","DOIUrl":"https://doi.org/10.12775/tmna.2022.069","url":null,"abstract":"We investigate the existence of multiple solutions\u0000for the $(p,q)$-quasilinear elliptic problem\u0000[\u0000begin{cases}\u0000-Delta_p u -Delta_q u = g(x, u) + varepsilon h(x,u)\u0000& mbox{in } Omega,\u0000u=0 & mbox{on } partialOmega,\u0000 end{cases}\u0000]\u0000where $1< p< q< +infty$, $Omega$ is an open bounded domain of\u0000${mathbb R}^N$, the nonlinearity $g(x,u)$ behaves at infinity as $|u|^{q-1}$,\u0000$varepsilonin{mathbb R}$ and $hin C(overlineOmegatimes{mathbb R},{mathbb R})$.\u0000In spite of the possible lack of a variational structure of this problem,\u0000from suitable assumptions on $g(x,u)$ and\u0000appropriate procedures and estimates,\u0000the existence of multiple solutions can be proved for small perturbations.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42577350","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
The fixed point set of the inverse involution on a Lie group 李群上逆对合的不动点集
IF 0.7 4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2023-02-26 DOI: 10.12775/tmna.2022.012
H. Duan, Shali Liu
{"title":"The fixed point set of the inverse involution on a Lie group","authors":"H. Duan, Shali Liu","doi":"10.12775/tmna.2022.012","DOIUrl":"https://doi.org/10.12775/tmna.2022.012","url":null,"abstract":"The inverse involution on a Lie group $G$ is the periodic $2$ transformation\u0000$gamma $ that sends each element $gin G$ to its inverse $g^{-1}$. The\u0000variety of the fixed point set $Fix(gamma )$ is of importance for the\u0000relevances with Morse function on the Lie group $G$, and the $G$-representations\u0000of the cyclic group $mathbb{Z}_{2}$. \u0000In this paper we develop an approach to calculate the diffeomorphism types of the fixed point sets $Fix(gamma)$ for the simple Lie groups.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48534835","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
Rank-two solenoidal endomorphisms 秩二螺线管自同态
IF 0.7 4区 数学
Topological Methods in Nonlinear Analysis Pub Date : 2023-02-26 DOI: 10.12775/tmna.2022.063
K. Ha, Jong Bum Lee
{"title":"Rank-two solenoidal endomorphisms","authors":"K. Ha, Jong Bum Lee","doi":"10.12775/tmna.2022.063","DOIUrl":"https://doi.org/10.12775/tmna.2022.063","url":null,"abstract":"Let $G$ be a torsion-free abelian group of rank two and let\u0000$phi$ be an endomorphism of $G$, called a rank-two emph{solenoidal endomorphism}.\u0000Then it is represented by a $2times 2$-matrix $M_phi$ with rational entries.\u0000The purpose of this article is to prove the following:\u0000The group, $mathrm{coker}(phi)$, of the cokernut of $phi$ is finite\u0000if and only if $M_phi$ is nonsingular, and if it is so, then\u0000we give an explicit formula for the order of $mathrm{coker}(phi)$, $[G:mathrm{im}(phi)]$,\u0000in terms of $p$-adic absolute values of the determinant of $M_phi$.\u0000Since $G$ is abelian, the Reidemeister number of $phi$ is equal to the order of the cokernut of $mathrm{id}-phi$ and, when it is finite, \u0000it is equal to the number of fixed points of the Pontryagin dual $widehatphi$ of $phi$.\u0000Thereby, we solve completely the problem raised in cite{Miles} of finding the possible sequences of periodic point counts\u0000for emph{all} endomorphisms of the rank-two solenoids.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43163203","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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