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Energy minimizing solutions to slightly subcritical elliptic problems on nonconvex polygonal domains 非凸多边形区域上微次临界椭圆问题的能量最小化解
3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231332
Woocheol Choi
{"title":"Energy minimizing solutions to slightly subcritical elliptic problems on nonconvex polygonal domains","authors":"Woocheol Choi","doi":"10.3934/math.20231332","DOIUrl":"https://doi.org/10.3934/math.20231332","url":null,"abstract":"<abstract><p>In this paper we are concerned with the Lane-Emden-Fowler equation</p> <p><disp-formula> <label/> <tex-math id=\"FE1\"> begin{document}$ begin{equation*} left{begin{array}{rll}-Delta u &amp;amp; = u^{frac{n+2}{n-2}- varepsilon}&amp;amp; {rm{in}}; Omega, u&amp;amp;&amp;gt;0&amp;amp; {rm{in}}; Omega, u&amp;amp; = 0&amp;amp; {rm{on}}; partial Omega, end{array} right. end{equation*} $end{document} </tex-math></disp-formula></p> <p>where $ Omega subset mathbb{R}^n $ ($ n geq 3 $) is a nonconvex polygonal domain and $ varepsilon &amp;gt; 0 $. We study the asymptotic behavior of minimal energy solutions as $ varepsilon &amp;gt; 0 $ goes to zero. A main part is to show that the solution is uniformly bounded near the boundary with respect to $ varepsilon &amp;gt; 0 $. The moving plane method is difficult to apply for the nonconvex polygonal domain. To get around this difficulty, we derive a contradiction after assuming that the solution blows up near the boundary by using the Pohozaev identity and the Green's function.</p></abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135400790","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 some properties of a generalized min matrix 关于广义最小矩阵的一些性质
3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231336
Emrah Polatlı
{"title":"On some properties of a generalized min matrix","authors":"Emrah Polatlı","doi":"10.3934/math.20231336","DOIUrl":"https://doi.org/10.3934/math.20231336","url":null,"abstract":"<abstract><p>In this paper, we investigate a min matrix and obtain its $ LU $-decomposition, determinant, permanent, inverse, and norm properties. In addition, we obtain a recurrence relation provided by the characteristic polynomial of this matrix. Finally, we present an example to illustrate the results obtained.</p></abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135440082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 instability of periodic solutions for a population model with cross-diffusion 具有交叉扩散的种群模型周期解的不稳定性
3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231529
Weiyu Li, Hongyan Wang
{"title":"The instability of periodic solutions for a population model with cross-diffusion","authors":"Weiyu Li, Hongyan Wang","doi":"10.3934/math.20231529","DOIUrl":"https://doi.org/10.3934/math.20231529","url":null,"abstract":"<abstract><p>This paper is concerned with a population model with prey refuge and a Holling type Ⅲ functional response in the presence of self-diffusion and cross-diffusion, and its Turing pattern formation problem of Hopf bifurcating periodic solutions was studied. First, we discussed the stability of periodic solutions for the ordinary differential equation model, and derived the first derivative formula of periodic functions for the perturbed model. Second, applying the Floquet theory, we gave the conditions of Turing patterns occurring at Hopf bifurcating periodic solutions. Additionally, we determined the range of cross-diffusion coefficients for the diffusive population model to form Turing patterns at the stable periodic solutions. Finally, our research was summarized and the relevant conclusions were simulated numerically.</p></abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135447502","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 extremal cacti with minimum Sombor index 在仙人掌的末端有最小的Sombor指数
3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231537
Qiaozhi Geng, Shengjie He, Rong-Xia Hao
{"title":"On the extremal cacti with minimum Sombor index","authors":"Qiaozhi Geng, Shengjie He, Rong-Xia Hao","doi":"10.3934/math.20231537","DOIUrl":"https://doi.org/10.3934/math.20231537","url":null,"abstract":"<abstract><p>Let $ H $ be a graph with edge set $ E_H $. The Sombor index and the reduced Sombor index of a graph $ H $ are defined as $ SO(H) = sumlimits_{uvin E_H}sqrt{d_{H}(u)^{2}+d_{H}(v)^{2}} $ and $ SO_{red}(H) = sumlimits_{uvin E_H}sqrt{(d_{H}(u)-1)^{2}+(d_{H}(v)-1)^{2}} $, respectively. Where $ d_{H}(u) $ and $ d_{H}(v) $ are the degrees of the vertices $ u $ and $ v $ in $ H $, respectively. A cactus is a connected graph in which any two cycles have at most one common vertex. Let $ mathcal{C}(n, k) $ be the class of cacti of order $ n $ with $ k $ cycles. In this paper, the lower bound for the Sombor index of the cacti in $ mathcal{C}(n, k) $ is obtained and the corresponding extremal cacti are characterized when $ ngeq 4k-2 $ and $ kgeq 2 $. Moreover, the lower bound of the reduced Sombor index of cacti is obtained by similar approach.</p></abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135506893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 pullback attractor for the 2D g-Navier-Stokes equation with nonlinear damping and time delay 具有非线性阻尼和时滞的二维g-Navier-Stokes方程的回拉吸引子
3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231363
Xiaoxia Wang, Jinping Jiang
{"title":"The pullback attractor for the 2D g-Navier-Stokes equation with nonlinear damping and time delay","authors":"Xiaoxia Wang, Jinping Jiang","doi":"10.3934/math.20231363","DOIUrl":"https://doi.org/10.3934/math.20231363","url":null,"abstract":"<abstract><p>In this article, the global well-posedness of weak solutions for 2D non-autonomous g-Navier-Stokes equations on some bounded domains were investigated by the Faedo-Galerkin method. Then the existence of pullback attractors for 2D g-Navier-Stokes equations with nonlinear damping and time delay was obtained using the method of pullback condition (PC).</p></abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135550335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
More on complex hesitant fuzzy graphs 更多关于复杂犹豫模糊图
3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231554
AbdUlazeez Alkouri, Eman A. AbuHijleh, Ghada Alafifi, Eman Almuhur, Fadi M. A. Al-Zubi
{"title":"More on complex hesitant fuzzy graphs","authors":"AbdUlazeez Alkouri, Eman A. AbuHijleh, Ghada Alafifi, Eman Almuhur, Fadi M. A. Al-Zubi","doi":"10.3934/math.20231554","DOIUrl":"https://doi.org/10.3934/math.20231554","url":null,"abstract":"<abstract><p>Correctly determining a company's market worth during an entire year or a certain period presents a difficulty to decision-makers. In the case of the merger of companies, the need performs heavier when both the companies' owners are attracted to establishing a fair price at the optimal time to merge. The effectiveness of representing, connecting and manipulating both uncertainty and periodicity information becomes highly required. Hence, study and nhance some properties and conditions of the algebraic structure of complex hesitant fuzzy graphs. Therefore, the degree of composition between two complex hesitant fuzzy graphs is proposed. Also, the formal definitions of union, joint and complement are presented to be covered in the realm of complex hesitant fuzzy graphs. A real-life application is illustrated to show the relation between vertices and edges in the form of complex hesitant fuzzy graphs.</p></abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135562867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Excess profit relative to the benchmark asset under the $ alpha $-confidence level 在$ alpha $-置信水平下相对于基准资产的超额利润
3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231553
Dong Ma, Peibiao Zhao, Minghan Lyu, Jun Zhao
{"title":"Excess profit relative to the benchmark asset under the $ alpha $-confidence level","authors":"Dong Ma, Peibiao Zhao, Minghan Lyu, Jun Zhao","doi":"10.3934/math.20231553","DOIUrl":"https://doi.org/10.3934/math.20231553","url":null,"abstract":"<abstract><p>We introduce a generalized concept of arbitrage, excess profit relative to the benchmark asset under $ alpha $-confidence level, $ alpha $-REP, in a single-period market model with proportional transaction costs. We obtain a fundamental theorem of asset pricing with respect to the absence of $ alpha $-REP. Moreover, we discuss the relationships between classical arbitrage, strong statistical arbitrage and $ alpha $-REP.</p></abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135562870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 generalization of Petryshyn's fixed point theorem and its application to the product of $ n $-nonlinear integral equations Petryshyn不动点定理的推广及其在n -非线性积分方程积中的应用
3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231562
Ateq Alsaadi, Manochehr Kazemi, Mohamed M. A. Metwali
{"title":"On generalization of Petryshyn's fixed point theorem and its application to the product of $ n $-nonlinear integral equations","authors":"Ateq Alsaadi, Manochehr Kazemi, Mohamed M. A. Metwali","doi":"10.3934/math.20231562","DOIUrl":"https://doi.org/10.3934/math.20231562","url":null,"abstract":"<abstract><p>Regarding the Hausdorff measure of noncompactness, we provide and demonstrate a generalization of Petryshyn's fixed point theorem in Banach algebras. Comparing this theorem to Schauder and Darbo's fixed point theorems, we can skip demonstrating closed, convex and compactness properties of the investigated operators. We employ our fixed point theorem to provide the existence findings for the product of $ n $-nonlinear integral equations in the Banach algebra of continuous functions $ C(I_a) $, which is a generalization of various types of integral equations in the literature. Lastly, a few specific instances and informative examples are provided. Our findings can successfully be extended to several Banach algebras, including $ AC, C^1 $ or $ BV $-spaces.</p></abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"137 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135610499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Analyzing a SEIR-Type mathematical model of SARS-COVID-19 using piecewise fractional order operators 基于分段分数阶算子的SARS-COVID-19 seir型数学模型分析
3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231382
Nadiyah Hussain Alharthi, Mdi Begum Jeelani
{"title":"Analyzing a SEIR-Type mathematical model of SARS-COVID-19 using piecewise fractional order operators","authors":"Nadiyah Hussain Alharthi, Mdi Begum Jeelani","doi":"10.3934/math.20231382","DOIUrl":"https://doi.org/10.3934/math.20231382","url":null,"abstract":"<abstract><p>Recently, the area devoted to mathematical epidemiology has attracted much attention. Mathematical formulations have served as models for various infectious diseases. In this regard, mathematical models have also been used to study COVID-19, a threatening disease in present time. This research work is devoted to consider a SEIR (susceptible-exposed-infectious-removed) type mathematical model for investigating COVID-19 alongside a new scenario of fractional calculus. We consider piece-wise fractional order derivatives to investigate the proposed model for qualitative and computational analysis. The results related to the qualitative analysis are studied via using the tools of fixed point approach. In addition, the computational analysis is performed due to a significance of simulation to understand the transmission dynamics of COVID-19 infection in the community. In addition, a numerical scheme based on Newton's polynomials is established to simulate the approximate solutions of the proposed model by using various fractional orders. Additionally, some real data results are also shown in comparison to the numerical results.</p></abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"112 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135653429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Mathematical modeling for the development of traffic based on the theory of system dynamics 基于系统动力学理论的交通发展数学建模
3区 数学
AIMS Mathematics Pub Date : 2023-01-01 DOI: 10.3934/math.20231413
Juan Manuel Sánchez, Adrián Valverde, Juan L. G. Guirao, Huatao Chen
{"title":"Mathematical modeling for the development of traffic based on the theory of system dynamics","authors":"Juan Manuel Sánchez, Adrián Valverde, Juan L. G. Guirao, Huatao Chen","doi":"10.3934/math.20231413","DOIUrl":"https://doi.org/10.3934/math.20231413","url":null,"abstract":"<abstract><p>This paper is concerned with mathematical modeling for the development of Shandong traffic. The system dynamics model of the development of traffic in Shandong is established. In terms of this model, it is shown that highway operation as well as rail transit promotes the development of traffic, while traffic accidents inhibit traffic development. Moreover, the maximum error between the output data and the statistics bureau, based on which some forecasts for the development of traffic in the future are given, is obtained, some suggestions and optimization schemes for traffic development are given. Finally, a neural network model of the development of Shandong traffic is also derived.</p></abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136053176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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