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Journal of Dynamics and Differential Equations最新文献

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Global Existence and Some Qualitative Properties of Weak Solutions for a Class of Heat Equations with a Logarithmic Nonlinearity in Whole $${mathbb {R}}^{N}$$ 全$${{mathbb {R}}^{N}$ 具有对数非线性的一类热方程弱解的全局存在性和一些定性性质
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-08-06 DOI: 10.1007/s10884-024-10385-4
Tahir Boudjeriou, Claudianor O. Alves
{"title":"Global Existence and Some Qualitative Properties of Weak Solutions for a Class of Heat Equations with a Logarithmic Nonlinearity in Whole $${mathbb {R}}^{N}$$","authors":"Tahir Boudjeriou, Claudianor O. Alves","doi":"10.1007/s10884-024-10385-4","DOIUrl":"https://doi.org/10.1007/s10884-024-10385-4","url":null,"abstract":"<p>This paper aims to investigate the global existence and uniqueness of weak solutions for a class of heat equations with logarithmic nonlinearity in <span>({mathbb {R}}^{N})</span>, as well as to examine some of their qualitative properties. Additionally, we analyze the boundedness and higher integrability of these solutions.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141931011","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
Traveling Wavefronts to a Model of Precursor and Differentiated Cells: Impacting Parameter-Structure Transition from Monostable to Bistable, and from Monotone to Non-monotone 前体细胞和分化细胞模型的移动波面：从单稳态到双稳态以及从单调到非单调的参数-结构转变的影响
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-08-06 DOI: 10.1007/s10884-024-10384-5
Yuanxi Yue, Chunhua Ou
{"title":"Traveling Wavefronts to a Model of Precursor and Differentiated Cells: Impacting Parameter-Structure Transition from Monostable to Bistable, and from Monotone to Non-monotone","authors":"Yuanxi Yue, Chunhua Ou","doi":"10.1007/s10884-024-10384-5","DOIUrl":"https://doi.org/10.1007/s10884-024-10384-5","url":null,"abstract":"<p>This paper provides a novel analysis of the rich and complex propagation dynamics to a model of precursor and differentiated cells, with the appearance of non-isolated equilibria on a line in the phase space. We established the existence of traveling waves in the monostable monotone case by means of continuation argument via perturbation in a weighted functional space, by applying the abstract implicit function theorem. We proved necessary and sufficient conditions of the minimal wave speed selection and showed the existence of the transition (turning point) <span>(k^*)</span> for the minimal wave speed when the parameters <span>(lambda )</span> and <span>(gamma )</span> are fixed. Two explicit estimates about <span>(k^*)</span> were given by the easy-to-apply theorem we derived. We investigated the decay rate of the minimal traveling wave as <span>(zrightarrow infty )</span> in terms of the value of <i>k</i>. We further proved the existence of non-negative wavefronts in the monostable non-monotone case and found that the minimal wave speed is always linearly selected. Finally in the bistable monotone case, the existence and uniqueness of bistable traveling waves were proved via constructing an auxiliary parabolic non-local equation.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141931008","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
Entropy for Three-dimensional Vector Fields 三维矢量场的熵
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-08-03 DOI: 10.1007/s10884-024-10383-6
Fei Li, Wanlou Wu
{"title":"Entropy for Three-dimensional Vector Fields","authors":"Fei Li, Wanlou Wu","doi":"10.1007/s10884-024-10383-6","DOIUrl":"https://doi.org/10.1007/s10884-024-10383-6","url":null,"abstract":"<p>In this paper, we show that for any <span>(C^1)</span> three-dimensional vector fields with positive topological entropy, the topological entropy can be approximated by horseshoes. Precisely, for any <span>(C^1)</span> three-dimensional vector field <i>X</i> with positive topological entropy, there exists a vector field <i>Y</i> arbitrarily close (in the <span>(C^1)</span> topology) to <i>X</i> exhibiting a horseshoe <span>(Lambda )</span> such that the topological entropy of <i>Y</i> restricted on <span>(Lambda )</span> can arbitrarily approximate the topological entropy of <i>X</i>. This extends a classical result (Katok in Inst Hautes Études Sci Publ Math 51:137–173, 1980) of Katok for <span>(C^{1+alpha }(alpha &gt;0))</span> surface diffeomorphisms and a result (Wu and Liu in Proc Am Math Soc 148(1):223–233, 2020) for <span>(C^1)</span> surface diffeomorphisms.\u0000</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141884929","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
Pinsker $$sigma $$ -Algebra Character and Mean Li–Yorke Chaos Pinsker $$sigma $$ -代数特性与平均李-约克混沌
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-07-22 DOI: 10.1007/s10884-024-10381-8
Chunlin Liu, Rongzhong Xiao, Leiye Xu
{"title":"Pinsker $$sigma $$ -Algebra Character and Mean Li–Yorke Chaos","authors":"Chunlin Liu, Rongzhong Xiao, Leiye Xu","doi":"10.1007/s10884-024-10381-8","DOIUrl":"https://doi.org/10.1007/s10884-024-10381-8","url":null,"abstract":"<p>Let <i>G</i> be an infinite countable discrete amenable group. For any <i>G</i>-action on a compact metric space <i>X</i>, it is proved that for any sequence <span>((G_n)_{nge 1})</span> consisting of non-empty finite subsets of <i>G</i> with <span>(lim _{nrightarrow infty }|G_n|=infty )</span>, Pinsker <span>(sigma )</span>-algebra is a characteristic factor for <span>((G_n)_{nge 1})</span>. As a consequence, for a class of <i>G</i>-topological dynamical systems, positive topological entropy implies mean Li–Yorke chaos along a class of sequences consisting of non-empty finite subsets of <i>G</i>.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744186","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
Entropy Spectrum of Lyapunov Exponents for Typical Cocycles 典型循环的李亚普诺夫指数熵谱
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-07-20 DOI: 10.1007/s10884-024-10379-2
Reza Mohammadpour
{"title":"Entropy Spectrum of Lyapunov Exponents for Typical Cocycles","authors":"Reza Mohammadpour","doi":"10.1007/s10884-024-10379-2","DOIUrl":"https://doi.org/10.1007/s10884-024-10379-2","url":null,"abstract":"<p>In this paper, we study the size of the level sets of all Lyapunov exponents. For typical cocycles, we establish a variational relation between the topological entropy of the level sets of Lyapunov exponents and the topological pressure of the generalized singular value function.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744188","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
Long-Time Behavior for Semilinear Equation with Time-Dependent and Almost Sectorial Linear Operator 具有时间依赖性和近似扇形线性算子的半线性方程的长时行为
IF 1.4 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-07-15 DOI: 10.1007/s10884-024-10378-3
Maykel Belluzi, Tomás Caraballo, Marcelo J. D. Nascimento, K. Schiabel
{"title":"Long-Time Behavior for Semilinear Equation with Time-Dependent and Almost Sectorial Linear Operator","authors":"Maykel Belluzi, Tomás Caraballo, Marcelo J. D. Nascimento, K. Schiabel","doi":"10.1007/s10884-024-10378-3","DOIUrl":"https://doi.org/10.1007/s10884-024-10378-3","url":null,"abstract":"","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141647480","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
Generalized Bounded Distortion Property 广义有界失真特性
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-07-05 DOI: 10.1007/s10884-024-10376-5
Gregory Borissov, Grigorii Monakov
{"title":"Generalized Bounded Distortion Property","authors":"Gregory Borissov, Grigorii Monakov","doi":"10.1007/s10884-024-10376-5","DOIUrl":"https://doi.org/10.1007/s10884-024-10376-5","url":null,"abstract":"<p>We prove the nonstationary bounded distortion property for <span>(C^{1 + varepsilon })</span> smooth dynamical systems on multidimensional spaces. The results we obtain are motivated by potential application to study of spectral properties of discrete Schrödinger operators with potentials generated by Sturmian sequences.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551893","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 Solutions for a Class of Nonlinear Differential Equations 一类非线性微分方程的周期性解法
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-07-02 DOI: 10.1007/s10884-024-10375-6
Huafeng Xiao, Juan Xiao, Jianshe Yu
{"title":"Periodic Solutions for a Class of Nonlinear Differential Equations","authors":"Huafeng Xiao, Juan Xiao, Jianshe Yu","doi":"10.1007/s10884-024-10375-6","DOIUrl":"https://doi.org/10.1007/s10884-024-10375-6","url":null,"abstract":"<p>In this paper, we address the existence and multiplicity of 2-periodic solutions to differential equations with a distributed delay of the form </p><span>$$begin{aligned} x^{prime }(t)=fBig [int _{t-1}^t gbig (x(s)big ) d sBig ],quad x in textbf{R}^N. end{aligned}$$</span><p>Combining Kaplan–Yorke’s method with pseudoindex theory, we estimate the number of periodic solutions when the equations are both resonant and nonresonant. More specifically, we define two indices using asymptotic linear coefficient matrices at the origin and at infinity. Then the lower bound on the number of periodic solutions to the equations is estimated by the indices. Finally, two examples are given to illustrate our results.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503065","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
Highly Non-contractive Iterated Function Systems on Euclidean Space Can Have an Attractor 欧几里得空间上的高度非契约迭代函数系统可以有一个吸引器
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-06-14 DOI: 10.1007/s10884-024-10367-6
Krzysztof Leśniak, Nina Snigireva, Filip Strobin, Andrew Vince
{"title":"Highly Non-contractive Iterated Function Systems on Euclidean Space Can Have an Attractor","authors":"Krzysztof Leśniak, Nina Snigireva, Filip Strobin, Andrew Vince","doi":"10.1007/s10884-024-10367-6","DOIUrl":"https://doi.org/10.1007/s10884-024-10367-6","url":null,"abstract":"<p>Iterated function systems (IFSs) and their attractors have been central to the theory of fractal geometry almost from its inception. Moreover, contractivity of the functions in the IFS has been central to the theory of iterated functions systems. If the functions in the IFS are contractions, then the IFS is guaranteed to have a unique attractor. The converse question, does the existence of an attractor imply that the IFS is contractive, originates in a 1959 work by Bessaga which proves a converse to the contraction mapping theorem. Although a converse is true in that case, it is known that it does not always hold for an IFS. In general, there do exist IFSs with attractors and which are not contractive. However, in the context of IFSs in Euclidean space, this question has been open. In this paper we show that a highly non-contractive iterated function system in Euclidean space can have an attractor. In order to do that, we introduce the concept of an <i>L</i>-expansive map, i.e., a map that has Lipschitz constant strictly greater than one under any remetrization. This is necessitated by the absence of positively expansive maps on the interval.\u0000</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503066","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
Semiflows Strongly Focusing Monotone with Respect to High-Rank Cones: I. Generic Dynamics 相对于高容锥强聚焦单调的半流：I. 一般动力学
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-06-12 DOI: 10.1007/s10884-024-10372-9
Lirui Feng
{"title":"Semiflows Strongly Focusing Monotone with Respect to High-Rank Cones: I. Generic Dynamics","authors":"Lirui Feng","doi":"10.1007/s10884-024-10372-9","DOIUrl":"https://doi.org/10.1007/s10884-024-10372-9","url":null,"abstract":"<p>We consider a smooth semiflow strongly focusing monotone with respect to a cone of rank <i>k</i> on a Banach space. We obtain its generic dynamics, that is, semiorbits with initial data from an open and dense subset of any open bounded set either are pseudo-ordered or convergent to an equilibrium. For the case <span>(k=1)</span>, it is the celebrated Hirsch’s Generic Convergence Theorem. For the case <span>(k=2)</span>, we obtain the generic Poincaré-Bendixson Theorem.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141502919","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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