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Variational Principle for Fixed-point Free Flow 定点自由流的变分原理
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-09-25 DOI: 10.1007/s10255-026-0134-x
Rui-ming Liang, Hao-yi Lei
{"title":"Variational Principle for Fixed-point Free Flow","authors":"Rui-ming Liang,&nbsp;Hao-yi Lei","doi":"10.1007/s10255-026-0134-x","DOIUrl":"10.1007/s10255-026-0134-x","url":null,"abstract":"<div><p>Let (<i>X, ϕ</i>) be a compact flow without fixed points. We define the packing topological entropy <i>h</i><span>\u0000 <sup><i>P</i></sup><sub>top</sub>\u0000 \u0000 </span>(<i>ϕ, K</i>) on subsets of <i>X</i> through considering all the possible reparametrizations of time. For fixed-point free flows, we prove the following result: for any non-empty compact subset <i>K</i> of <i>X</i></p><div><div><span>$$h_{text{top}}^{P}(phi, K) = sup left{overline{h}_{mu}(phi) : mu(K) = 1, mu, text{is}, text{a}, text{Borel}, text{probability}, text{measure}, text{on}, Xright},$$</span></div></div><p>where <span>(overline{h}_{mu}(phi))</span> denotes the upper local entropy for a Borel probability measure <i>μ</i> on <i>X</i>.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 4","pages":"1245 - 1255"},"PeriodicalIF":0.9,"publicationDate":"2026-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149028965","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
On the Existence of Ground State Solutions for Choquard Systems with Nonlinear Couplings 非线性耦合乔库德系统基态解的存在性
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-09-25 DOI: 10.1007/s10255-026-0132-z
Li-ping Xu, Hai-bo Chen
{"title":"On the Existence of Ground State Solutions for Choquard Systems with Nonlinear Couplings","authors":"Li-ping Xu,&nbsp;Hai-bo Chen","doi":"10.1007/s10255-026-0132-z","DOIUrl":"10.1007/s10255-026-0132-z","url":null,"abstract":"<div><p>In this paper, we investigate the following coupled nonlinear Choquard system:</p><div><div><span>$$begin{cases}-Delta u + V_1(x)u = (J_{mu}(x) ast vert uvert^p)vert uvert^{p-2}u + beta vert uvert^{q-1}vert vvert^q quad text{in}, mathbb{R}^N,-Delta v + V_2(x)v = (J_{mu}(x) ast vert vvert^p)vert vvert^{p-2}v + beta vert vvert^{q-1}vert uvert^q quad text{in}, mathbb{R}^N,u,, v in H^1(mathbb{R}^N),end{cases}$$</span></div></div><p>where <span>(N geq 3, 0 &lt; mu &lt; N, frac{2N-mu}{N} &lt; p &lt; frac{2N-mu}{N-2}, 1 &lt; q &lt; p, beta &gt; 0)</span> is a coupling parameter, and <i>J</i><sub><i>μ</i></sub>(<i>x</i>) is convolution kernel, and <i>V</i><sub><i>i</i></sub>(<i>x</i>) is nonnegative continuous external potential for <i>i</i> = 1, 2. Using the Poho<i>ž</i>aev-Nehari manifold method, we establish the existence of positive ground state solutions for the system. Furthermore, we prove a nonexistence result for nontrivial solutions under certain conditions.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 4","pages":"1200 - 1224"},"PeriodicalIF":0.9,"publicationDate":"2026-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149028964","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
Unbounded Solutions of Third-order Infinite Interval Problems Relevant to the Laminar Mixing Layer 有关层流混合层的三阶无限区间问题的无界解
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-09-25 DOI: 10.1007/s10255-026-0135-9
Ming-he Pei, Li-bo Wang, Xue-zhe Lv
{"title":"Unbounded Solutions of Third-order Infinite Interval Problems Relevant to the Laminar Mixing Layer","authors":"Ming-he Pei,&nbsp;Li-bo Wang,&nbsp;Xue-zhe Lv","doi":"10.1007/s10255-026-0135-9","DOIUrl":"10.1007/s10255-026-0135-9","url":null,"abstract":"<div><p>In this paper, we consider the existence, uniqueness, and qualitative properties of solutions of nonlinear third-order two-point boundary value problems on the half-line by using the shooting method together with the Bolzano’s theorem and the maximum principle. Meanwhile, the nonlinear third-order three-point boundary value problems on the whole real line are studied by employing the matching method. As applications, we present the existence, uniqueness, and qualitative properties of solutions of the Blasius equations <i>u</i>‴+<i>uu</i>″ = 0 with one of the following boundary conditions</p><div><div><span>$$begin{aligned}&amp;u^{prime}(-infty)=C, u(0)=0, u^{prime}(+infty)=1, qquadtext{with}; 0 leq C&lt; 1,&amp;u^{prime}(-infty)=C, u^{primeprimeprime}(0)=0, u^{prime}(+infty)=1, quad;,,text{with}; 0 leq C &lt; 1,end{aligned}$$</span></div></div><p>which arise from the laminar mixing layer between two parallel flows with different velocities.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 4","pages":"1409 - 1430"},"PeriodicalIF":0.9,"publicationDate":"2026-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149027602","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 Multi-birth Property of Markov Branching Processes with Immigration 具有迁移的马尔可夫分支过程的多生性
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-09-25 DOI: 10.1007/s10255-026-0133-y
Yan-yun Li, Jun-ping Li
{"title":"The Multi-birth Property of Markov Branching Processes with Immigration","authors":"Yan-yun Li,&nbsp;Jun-ping Li","doi":"10.1007/s10255-026-0133-y","DOIUrl":"10.1007/s10255-026-0133-y","url":null,"abstract":"<div><p>In this paper, we consider the multi-birth property of Markov branching processes with immigration. The joint probability generating function of multi-birth numbers for Markov branching processes with immigration until time <i>t</i> is obtained by constructing a new <i>Q</i>-process. In particular, the probability generating function of multi-birth number is also obtained for Markov branching processes until its extinction.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 4","pages":"1225 - 1244"},"PeriodicalIF":0.9,"publicationDate":"2026-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149027655","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
Insider Trading with Different Risk Preference on a Dynamic Risky Asset 动态风险资产的不同风险偏好内幕交易
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-09-25 DOI: 10.1007/s10255-024-1039-1
Kai Xiao, Yong-hui Zhou
{"title":"Insider Trading with Different Risk Preference on a Dynamic Risky Asset","authors":"Kai Xiao,&nbsp;Yong-hui Zhou","doi":"10.1007/s10255-024-1039-1","DOIUrl":"10.1007/s10255-024-1039-1","url":null,"abstract":"<div><p>For an insider trading model of a risky asset whose value is driven by an arithmetic Brownian motion, we establish a closed form of linear Bayesian equilibrium with a risk-neutral insider and a closed form of linear Bayesian equilibrium with a risk-averse insider respectively. It shows that (i) as time goes by, in the former equilibrium, residual information decreases but price pressure keeps constant, while in the latter, both residual information and price pressure decrease; (ii) as the insider becomes less and less risk-averse, the risk-averse equilibrium converges to the risk-neutral one; and (iii) when the volatility of the asset value goes to zero, the risk-averse equilibrium converges to the risk-averse one with a static risky asset in [Cho, K. Continuous auctions and insider trading. <i>Finance and Stochastics</i>, 7: 47–71 (2003)].</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 4","pages":"1184 - 1199"},"PeriodicalIF":0.9,"publicationDate":"2026-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149027668","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
Global Stability Analysis and Optimal Control for a Dynamical Model with Asymptomatic Infectious State 具有无症状传染状态的动态模型的全局稳定性分析与最优控制
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-08-22 DOI: 10.1007/s10255-026-0129-7
Shu-ping Li, Yu-ru Yuan, Rui-xia Zhang
{"title":"Global Stability Analysis and Optimal Control for a Dynamical Model with Asymptomatic Infectious State","authors":"Shu-ping Li,&nbsp;Yu-ru Yuan,&nbsp;Rui-xia Zhang","doi":"10.1007/s10255-026-0129-7","DOIUrl":"10.1007/s10255-026-0129-7","url":null,"abstract":"<div><p>In this paper, we present a dynamical model with asymptomatic infections and optimal control strategies based on a regular network. The basic model without control and basic mathematical results are obtained. Firstly, we obtain the basic reproduction number by using the method of the next generation matrix. Secondly, by taking advantage of the Lyapunov function, we prove that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number <i>R</i><sub>0</sub> &lt; 1. By using generalized Bendixson-Dulac thereom, we prove that the unique endemic equilibrium is globally asymptotically stable when <i>R</i><sub>0</sub> &gt; 1. In addition, by using Pon-tryagin’s maximum principle, several reasonable optimal control strategies are suggested to the prevention and control the disease. Finally, numerical simulations are presented to verify the above theoretical results, and we perform sensitivity analysis by partial rank correlation coefficient(PRCC) methods. It is worth noting that asymptomatic infections have a greater contribution to the epidemic of diseases.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 4","pages":"1256 - 1268"},"PeriodicalIF":0.9,"publicationDate":"2026-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149027656","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
Exact Periodic Solutions of a Kind of Quintic Nonlinear Liénard Equation and Their Evolution with Hamilton Energy 一类五次非线性lisamadard方程的精确周期解及其随Hamilton能量的演化
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-08-22 DOI: 10.1007/s10255-026-0122-1
Wei-guo Zhang, Yu-li Guo, Shao-wei Li, Xue Zhang
{"title":"Exact Periodic Solutions of a Kind of Quintic Nonlinear Liénard Equation and Their Evolution with Hamilton Energy","authors":"Wei-guo Zhang,&nbsp;Yu-li Guo,&nbsp;Shao-wei Li,&nbsp;Xue Zhang","doi":"10.1007/s10255-026-0122-1","DOIUrl":"10.1007/s10255-026-0122-1","url":null,"abstract":"<div><p>In this paper, we study the exact periodic solutions of a kind of Liénard equation with cubic and quintic nonlinearities and the evolution of periodic solutions with Hamilton energy. Firstly, the qualitative analysis of the equation is carried out by using the dynamic system theorem, then the existence conditions, the number and the approximate positions of the periodic solutions and other bounded solutions for this equation are given. By applying the analysis approach on the basis of the first integral and several appropriate transformations, we obtain all seven families of elliptic function periodic solutions of the equation under different parameters conditions. By studying the limit of these periodic solutions on the Hamilton energy evolution and directly using the analysis approach based on the first integral, all ten pairs of bell-shaped solutions and kinkshaped solutions (corresponding to homoclinic and heteroclinic orbits) for the studied equation under different parameter conditions are also given. In this paper, we establish the relationship between the Hamilton energy of the system and the periodic solution, bell-shaped solution and kink-shaped solution of the system. From the analysis in this paper, it can be seen that the reason why the Liénard equation we studied has periodic solutions, bell-shaped solutions and kink-shaped solutions is essentially determined by the energy value-taken of the Hamilton system corresponding to the equation in different ranges. As the preliminary application of the results in this paper, the periodic wave solutions and the solitary wave solutions of the typical Ablowitz equation are also given.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 4","pages":"1068 - 1103"},"PeriodicalIF":0.9,"publicationDate":"2026-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149028963","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
Lyapunov Exponents of Discrete Analytic Schrödinger Equations with Multivariable Gevrey Perturbation 具有多变量Gevrey摄动的离散解析Schrödinger方程的Lyapunov指数
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-07-15 DOI: 10.1007/s10255-026-0091-4
Kai Tao
{"title":"Lyapunov Exponents of Discrete Analytic Schrödinger Equations with Multivariable Gevrey Perturbation","authors":"Kai Tao","doi":"10.1007/s10255-026-0091-4","DOIUrl":"10.1007/s10255-026-0091-4","url":null,"abstract":"<div><p>In the study of the continuity of the Lyapunov exponent for the discrete quasi-periodic Schrödinger operators, there is a pioneering result by Wang-You that the authors constructed the examples whose Lyapunov exponent is discontinuous in the potential with the <i>C</i><sup>0</sup> norm for non-analytic potentials. In this paper, we consider these operators for some Gevrey potential, which is an analytic function with a Gevrey small perturbation on the multi-dimensional torus. We prove that in the large coupling regions, the Lyapunov exponent is positive and jointly continuous with the <i>C</i><sup>0</sup> norm in all parameters, such as the energy, the frequency and the potential, for two transformations, the multi-frequency shift and the skew shift. It is complementary to Wang-You’s result.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 3","pages":"1025 - 1042"},"PeriodicalIF":0.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458901","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 Heat Flow with Nonzero Potential for a Critical Trudinger-Moser Functional 临界Trudinger-Moser泛函的非零势热流
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-07-15 DOI: 10.1007/s10255-024-1082-y
Peng-xiu Yu
{"title":"A Heat Flow with Nonzero Potential for a Critical Trudinger-Moser Functional","authors":"Peng-xiu Yu","doi":"10.1007/s10255-024-1082-y","DOIUrl":"10.1007/s10255-024-1082-y","url":null,"abstract":"<div><p>Let Ω ⊂ ℝ<sup>2</sup> be a smooth bounded domain and <i>H</i><span>\u0000 <sup>0</sup><sub>1</sub>\u0000 \u0000 </span>(Ω) be the standard Sobolev space consisting of functions which vanish on ∂Ω and whose gradient is in <i>L</i><sup>2</sup>(Ω). In this paper, we investigate critical points of the Trudinger-Moser functional by a heat flow. Our method is based on blow-up analysis, relying on integral estimates.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 3","pages":"957 - 968"},"PeriodicalIF":0.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458756","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
Partial Inverse Nodal Problems for Eigenparameter Dependent Sturm-Liouville Problems 特征参数相关Sturm-Liouville问题的部分逆节点问题
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-07-15 DOI: 10.1007/s10255-026-0092-3
Dong-Jie Wu, Chuan-Fu Yang, Murat Sat
{"title":"Partial Inverse Nodal Problems for Eigenparameter Dependent Sturm-Liouville Problems","authors":"Dong-Jie Wu,&nbsp;Chuan-Fu Yang,&nbsp;Murat Sat","doi":"10.1007/s10255-026-0092-3","DOIUrl":"10.1007/s10255-026-0092-3","url":null,"abstract":"<div><p>In this work, we are concerned with inverse nodal problems of Sturm-Liouville operators with eigenparameter dependent boundary conditions on the interval [0, 1]. It is shown that a twin dense subset of the nodal set in a subinterval <span>([a_1,a_2]subset[0,1], (a_1&lt;tfrac{1}{2}&lt;a_2))</span> uniquely determines all parameters of the boundary conditions and the potential (up to a constant) on the interval [0, 1].</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 3","pages":"1013 - 1024"},"PeriodicalIF":0.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458902","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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