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Infinitely Many Solutions for a Class of Quasi-linear Elliptic Problem 一类准线性椭圆问题的无限多解
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-05 DOI: 10.1007/s10255-024-1091-x
Xiao-yao Jia, Zhen-luo Lou
{"title":"Infinitely Many Solutions for a Class of Quasi-linear Elliptic Problem","authors":"Xiao-yao Jia,&nbsp;Zhen-luo Lou","doi":"10.1007/s10255-024-1091-x","DOIUrl":"10.1007/s10255-024-1091-x","url":null,"abstract":"<div><p>In this paper, we study the following quasi-linear elliptic equation</p><div><div><span>$$left{{matrix{{- ,{rm{div(}}phi {rm{(}}left| {nabla u} right|{rm{)}}nabla u{rm{) = lambda}}psi {rm{(}}left| u right|{rm{)}}u + ,varphi {rm{(}}left| u right|{rm{)}}u,,,,,{rm{in}},,,Omega,,,,} cr {u = 0,,,,,,,,{rm{on}},,partial Omega {rm{,}},,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,} cr}} right.$$</span></div></div><p>where Ω ⊂ ℝ<sup><i>N</i></sup> is a bounded domain, λ &gt; 0 is a parameter. The function <i>ψ</i>(∣<i>t</i>∣)<i>t</i> is the subcritical term, and <i>ϕ</i>(∣<i>t</i>∣)<i>t</i> is the critical Orlicz-Sobolev growth term with respect to <i>φ</i>. Under appropriate conditions on <i>φ</i>, <i>ψ</i> and <i>ϕ</i>, we prove the existence of infinitely many weak solutions for quasi-linear elliptic equation, for <i>λ</i> ∈ (0, <i>λ</i><sub>0</sub>), where <i>λ</i><sub>0</sub> &gt; 0 is a fixed constant.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256449","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 Phase Portraits of Uniform Isochronous Centers System of Degree Six with Polynomial Commutator 具有多项式换向器的六度均匀等时中心系统的全局相位特征
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-05 DOI: 10.1007/s10255-024-1081-z
Li-na Guo, Ai-yong Chen, Shuai-feng Zhao
{"title":"Global Phase Portraits of Uniform Isochronous Centers System of Degree Six with Polynomial Commutator","authors":"Li-na Guo,&nbsp;Ai-yong Chen,&nbsp;Shuai-feng Zhao","doi":"10.1007/s10255-024-1081-z","DOIUrl":"10.1007/s10255-024-1081-z","url":null,"abstract":"<div><p>This paper studies the global phase portraits of uniform isochronous centers system of degree six with polynomial commutator. Such systems have the form <span>(dot x = - y + xf(x,,y),,,dot y = x + yf(x,,y))</span>, where <i>f</i>(<i>x, y</i>) = <i>a</i><sub>1</sub><i>x</i> + <i>a</i><sub>2</sub><i>xy</i> + <i>a</i><sub>3</sub><i>xy</i><sup>2</sup> + <i>a</i><sub>4</sub><i>xy</i><sup>3</sup> + <i>a</i><sub>5</sub><i>xy</i><sup>4</sup> = <i>xσ</i>(<i>y</i>), and any zero of 1 + <i>a</i><sub>1</sub><i>y</i> + <i>a</i><sub>2</sub><i>y</i><sup>2</sup> + <i>a</i><sub>3</sub><i>y</i><sup>3</sup> + <i>a</i><sub>4</sub><i>y</i><sup>4</sup> + <i>a</i><sub>5</sub><i>y</i><sup>5</sup>, <span>(y = bar y)</span> is an invariant straight line. At last, all global phase portraits are drawn on the Poincaré disk.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10255-024-1081-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Derivation of Expanded Isospectral-Nonisospectral Integrable Hierarchies via the Column-vector Loop Algebra 通过柱向量环代数推导扩展等谱-非等谱可积分层次结构
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-05 DOI: 10.1007/s10255-024-1047-1
Hai-feng Wang, Yu-feng Zhang
{"title":"Derivation of Expanded Isospectral-Nonisospectral Integrable Hierarchies via the Column-vector Loop Algebra","authors":"Hai-feng Wang,&nbsp;Yu-feng Zhang","doi":"10.1007/s10255-024-1047-1","DOIUrl":"10.1007/s10255-024-1047-1","url":null,"abstract":"<div><p>A scheme for generating nonisospectral integrable hierarchies is introduced. Based on the method, we deduce a nonisospectral hierarchy of soliton equations by considering a linear spectral problem. It follows that the corresponding expanded isospectral and nonisospectral integrable hierarchies are deduced based on a 6 dimensional complex linear space <span>(widetilde{mathbb{C}}^{6})</span>. By reducing these integrable hierarchies, we obtain the expanded isospectral and nonisospectral derivative nonlinear Schrödinger equation. By using the trace identity, the bi-Hamiltonian structure of these two hierarchies are also obtained. Moreover, some symmetries and conserved quantities of the resulting hierarchy are discussed.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256096","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
Optimal Timing of Business Conversion for Solvency Improvement 改善偿付能力的最佳业务转型时机
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-05 DOI: 10.1007/s10255-024-1048-0
Peng Li, Ming Zhou
{"title":"Optimal Timing of Business Conversion for Solvency Improvement","authors":"Peng Li,&nbsp;Ming Zhou","doi":"10.1007/s10255-024-1048-0","DOIUrl":"10.1007/s10255-024-1048-0","url":null,"abstract":"<div><p>In this paper, we study the optimal timing to convert the risk of business for an insurance company in order to improve its solvency. The cash flow of company evolves according to a jump-diffusion process. Business conversion option offers the company an opportunity to transfer the jump risk business out. In exchange for this option, the company needs to pay both fixed and proportional transaction costs. The proportional cost can also be seen as the profit loading of the jump risk business. We formulated this problem as an optimal stopping problem. By solving this stopping problem, we find that the optimal timing of business conversion mainly depends on the profit loading of the jump risk business. A larger profit loading would make the conversion option valueless. The fixed cost, however, only delays the optimal timing of business conversion. In the end, numerical results are provided to illustrate the impacts of transaction costs and environmental parameters to the optimal strategies.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256103","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 Degree Condition for Graphs Having All (a, b)-parity Factors 具有所有 (a, b) 奇偶因子的图的度条件
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-05 DOI: 10.1007/s10255-024-1090-y
Hao-dong Liu, Hong-liang Lu
{"title":"A Degree Condition for Graphs Having All (a, b)-parity Factors","authors":"Hao-dong Liu,&nbsp;Hong-liang Lu","doi":"10.1007/s10255-024-1090-y","DOIUrl":"10.1007/s10255-024-1090-y","url":null,"abstract":"<div><p>Let <i>a</i> and <i>b</i> be positive integers such that <i>a</i> ≤ <i>b</i> and <i>a</i> ≡ <i>b</i> (mod 2). We say that <i>G</i> has all (<i>a, b</i>)-parity factors if <i>G</i> has an <i>h</i>-factor for every function <i>h</i>: <i>V</i>(<i>G</i>) → {<i>a, a</i> + 2, ⋯, <i>b</i> − 2, <i>b</i>} with <i>b</i>∣<i>V</i>(<i>G</i>)∣ even and <i>h</i>(<i>v</i>) ≡ <i>b</i> (mod 2) for all <i>v</i> ∈ <i>V</i>(<i>G</i>). In this paper, we prove that every graph <i>G</i> with <i>n</i> ≥ 2(<i>b</i> + 1)(<i>a</i> + <i>b</i>) vertices has all (<i>a, b</i>)-parity factors if <i>δ</i>(<i>G</i>) ≥ (<i>b</i><sup>2</sup> − <i>b</i>)/<i>a</i>, and for any two nonadjacent vertices <span>(u,,v, in ,V,(G),,max {{d_G}(u),,{d_G}(v)} , ge {{bn} over {a + b}})</span>. Moreover, we show that this result is best possible in some sense.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256211","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 Strong Approximation for a Simple Reentrant Line in Light Traffic Under First-buffer First-served Service Discipline 论 "先缓冲先服务 "纪律下轻度交通中简单重入线的强近似值
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-05 DOI: 10.1007/s10255-024-1093-8
Kai-ming Yang, Yong-jiang Guo
{"title":"On the Strong Approximation for a Simple Reentrant Line in Light Traffic Under First-buffer First-served Service Discipline","authors":"Kai-ming Yang,&nbsp;Yong-jiang Guo","doi":"10.1007/s10255-024-1093-8","DOIUrl":"10.1007/s10255-024-1093-8","url":null,"abstract":"<div><p>For a 2-station and 3-class reentrant line under first-buffer first-served (FBFS) service discipline in light traffic, we firstly construct the strong approximations for performance measures including the queue length, workload, busy time and idle time processes. Based on the obtained strong approximations, we use a strong approximation method to find all the law of the iterated logarithms (LILs) for the above four performance measures, which are expressed as some functions of system parameters: means and variances of interarrival and service times, and characterize the fluctuations around their fluid approximations.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256633","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
Strong Limit Theorems for Weighted Sums under the Sub-linear Expectations 次线性期望下加权和的强极限定理
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-05 DOI: 10.1007/s10255-024-1127-2
Feng-xiang Feng, Ding-cheng Wang, Qun-ying Wu, Hai-wu Huang
{"title":"Strong Limit Theorems for Weighted Sums under the Sub-linear Expectations","authors":"Feng-xiang Feng,&nbsp;Ding-cheng Wang,&nbsp;Qun-ying Wu,&nbsp;Hai-wu Huang","doi":"10.1007/s10255-024-1127-2","DOIUrl":"10.1007/s10255-024-1127-2","url":null,"abstract":"<div><p>In this article, we study strong limit theorems for weighted sums of extended negatively dependent random variables under the sub-linear expectations. We establish general strong law and complete convergence theorems for weighted sums of extended negatively dependent random variables under the sub-linear expectations. Our results of strong limit theorems are more general than some related results previously obtained by Thrum (1987), Li et al. (1995) and Wu (2010) in classical probability space.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256192","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
Sliced Average Variance Estimation for Tensor Data 张量数据的切分平均方差估计
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-05 DOI: 10.1007/s10255-024-1024-8
Chuan-quan Li, Pei-wen Xiao, Chao Ying, Xiao-hui Liu
{"title":"Sliced Average Variance Estimation for Tensor Data","authors":"Chuan-quan Li,&nbsp;Pei-wen Xiao,&nbsp;Chao Ying,&nbsp;Xiao-hui Liu","doi":"10.1007/s10255-024-1024-8","DOIUrl":"10.1007/s10255-024-1024-8","url":null,"abstract":"<div><p>Tensor data have been widely used in many fields, e.g., modern biomedical imaging, chemometrics, and economics, but often suffer from some common issues as in high dimensional statistics. How to find their low-dimensional latent structure has been of great interest for statisticians. To this end, we develop two efficient tensor sufficient dimension reduction methods based on the sliced average variance estimation (SAVE) to estimate the corresponding dimension reduction subspaces. The first one, entitled tensor sliced average variance estimation (TSAVE), works well when the response is discrete or takes finite values, but is not <span>(sqrt n)</span> consistent for continuous response; the second one, named bias-correction tensor sliced average variance estimation (CTSAVE), is a de-biased version of the TSAVE method. The asymptotic properties of both methods are derived under mild conditions. Simulations and real data examples are also provided to show the superiority of the efficiency of the developed methods.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256217","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 Normalized Solutions for Nonlinear Biharmonic Schrödinger Equations in ℝN with L2-Subcritical Growth 具有 L2 次临界增长的ℝN 中非线性双谐波薛定谔方程的多重归一化解决方案
IF 0.8 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-01 DOI: 10.1007/s10255-024-1131-6
Jun Wang, Li Wang, Ji-xiu Wang
{"title":"Multiple Normalized Solutions for Nonlinear Biharmonic Schrödinger Equations in ℝN with L2-Subcritical Growth","authors":"Jun Wang, Li Wang, Ji-xiu Wang","doi":"10.1007/s10255-024-1131-6","DOIUrl":"https://doi.org/10.1007/s10255-024-1131-6","url":null,"abstract":"<p>In this article, we consider the existence of normalized solutions for the following nonlinear biharmonic Schrödinger equations</p><span>$$left{{matrix{{{Delta ^2}u = lambda u + hleft({varepsilon x} right),fleft(u right),} &amp; {x in mathbb{R}{^N},} cr {int_{mathbb{R}{^N}} {{{left| u right|}^2}dx = {c^2},}} &amp; {x in mathbb{R}{^N},} cr}} right.$$</span><p>where <i>c, ε</i> &gt; 0; <i>N</i> ≥ 5; <i>λ</i> ∈ ℝ is a Lagrange multiplier and is unknown, <i>h</i> ∈ <i>C</i>(ℝ<sup><i>N</i></sup>; [0;∞)); <i>f</i>: ℝ → ℝ is continuous function satisfying <i>L</i><sup>2</sup>-subcritical growth. When <i>ε</i> is small enough, we get multiple normalized solutions. Moreover, we also obtain orbital stability of the solutions.</p>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192338","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
Sharp Interface Limit for the One-dimensional Compressible Navier-Stokes/Allen-Cahn System with Composite Waves 具有复合波的一维可压缩纳维-斯托克斯/阿伦-卡恩系统的锐界面极限
IF 0.8 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-01 DOI: 10.1007/s10255-024-1130-7
Ya-zhou Chen, Yi Peng, Xiao-ding Shi
{"title":"Sharp Interface Limit for the One-dimensional Compressible Navier-Stokes/Allen-Cahn System with Composite Waves","authors":"Ya-zhou Chen, Yi Peng, Xiao-ding Shi","doi":"10.1007/s10255-024-1130-7","DOIUrl":"https://doi.org/10.1007/s10255-024-1130-7","url":null,"abstract":"<p>This paper is concerned with the sharp interface limit of Cauchy problem for the one-dimensional compressible Navier-Stokes/Allen-Cahn system with a composite wave consisting of the superposition of a rarefaction wave and a shock wave. Under the assumption that the viscosity coefficient and the reciprocal of mobility coefficient are directly proportional to the interface thickness, we first convert the sharp interface limit of the system into the large time behavior of the composite wave via a natural scaling. Then we prove that the composite wave is asymptotically stable under the small initial perturbations and the small strength of the rarefaction and shock wave. Finally, we show the solution of the Cauchy problem exists for all time, and converges to the composite wave solution of the corresponding Euler equations as the thickness of the interface tends to zero. The proof is mainly based on the energy method and the relative entropy.</p>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141198275","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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