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Nonautonomous Dynamical Systems最新文献

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The stability of nonlinear delay integro-differential equations in the sense of Hyers-Ulam Hyers-Ulam意义下非线性时滞积分-微分方程的稳定性
Nonautonomous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.1515/msds-2022-0169
J. Graef, C. Tunç, Merve Şengun, O. Tunç
{"title":"The stability of nonlinear delay integro-differential equations in the sense of Hyers-Ulam","authors":"J. Graef, C. Tunç, Merve Şengun, O. Tunç","doi":"10.1515/msds-2022-0169","DOIUrl":"https://doi.org/10.1515/msds-2022-0169","url":null,"abstract":"Abstract In this study, an initial-value problem for a nonlinear Volterra functional integro-differential equation on a finite interval was considered. The nonlinear term in the equation contains multiple time delays. In addition to giving some new theorems on the existence and uniqueness of solutions to the equation, the authors also prove the Hyers-Ulam-Rassias stability and the Hyers-Ulam stability of the equation. The proofs use several different tools including Banach’s fixed point theorem, the construction of a Picard operator, and an application of Pachpatte’s inequality. An example is provided to illustrate the existence, uniqueness, and stability properties of solutions.","PeriodicalId":30985,"journal":{"name":"Nonautonomous Dynamical Systems","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45342073","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Generalized BDSDEs driven by fractional Brownian motion 分数布朗运动驱动的广义BDSDEs
Nonautonomous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.1515/msds-2022-0167
Sadibou Aidara, Assane Ndiaye, Ahmadou Bamba Sow
{"title":"Generalized BDSDEs driven by fractional Brownian motion","authors":"Sadibou Aidara, Assane Ndiaye, Ahmadou Bamba Sow","doi":"10.1515/msds-2022-0167","DOIUrl":"https://doi.org/10.1515/msds-2022-0167","url":null,"abstract":"Abstract This article deals with a class of generalized backward doubly stochastic differential equations driven by fractional Brownian motion with the Hurst parameter <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>H</m:mi> </m:math> H greater than 1/2. The existence and uniqueness of solutions to our equation as well as comparison theorems are obtained.","PeriodicalId":30985,"journal":{"name":"Nonautonomous Dynamical Systems","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":"135497766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quasilinear class of noncoercive parabolic problems with Hardy potential and L1-data 一类具有Hardy势和l1数据的拟线性非强制抛物问题
Nonautonomous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.1515/msds-2022-0168
Taghi Ahmedatt, Youssef Hajji, H. Hjiaj
{"title":"Quasilinear class of noncoercive parabolic problems with Hardy potential and L1-data","authors":"Taghi Ahmedatt, Youssef Hajji, H. Hjiaj","doi":"10.1515/msds-2022-0168","DOIUrl":"https://doi.org/10.1515/msds-2022-0168","url":null,"abstract":"Abstract In this article, we study the following noncoercive quasilinear parabolic problem ∂ u ∂ t − div a ( x , t , u , ∇ u ) + ν ∣ u ∣ s − 1 u = λ ∣ u ∣ p − 2 u ∣ x ∣ p + f in Q T , u = 0 on Σ T , u ( x , 0 ) = u 0 in Ω , left{begin{array}{ll}frac{partial u}{partial t}-hspace{0.1em}text{div}hspace{0.1em}aleft(x,t,u,nabla u)+nu {| u| }^{s-1}u=lambda frac{{| u| }^{p-2}u}{{| x| }^{p}}+f& hspace{0.1em}text{in}hspace{0.1em}hspace{0.33em}{Q}_{T}, u=0& hspace{0.1em}text{on}hspace{0.1em}hspace{0.33em}{Sigma }_{T}, uleft(x,0)={u}_{0}& hspace{0.1em}text{in}hspace{0.1em}hspace{0.33em}Omega ,end{array}right. with f ∈ L 1 ( Q T ) fin {L}^{1}left({Q}_{T}) and u 0 ∈ L 1 ( Ω ) {u}_{0}in {L}^{1}left(Omega ) and show the existence of entropy solutions for this noncoercive parabolic problem with Hardy potential and L1-data.","PeriodicalId":30985,"journal":{"name":"Nonautonomous Dynamical Systems","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41752455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence results for some generalized Sigmoid Beverton-Holt models in time scales 时间尺度上一些广义Sigmoid Beverton-Holt模型的存在性结果
Nonautonomous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.1515/msds-2022-0166
Mariem Mohamed Abdelahi, Mohamed Ahmed Sambe, Elkhomeini Moulay Ely
{"title":"Existence results for some generalized Sigmoid Beverton-Holt models in time scales","authors":"Mariem Mohamed Abdelahi, Mohamed Ahmed Sambe, Elkhomeini Moulay Ely","doi":"10.1515/msds-2022-0166","DOIUrl":"https://doi.org/10.1515/msds-2022-0166","url":null,"abstract":"Abstract In this article, we investigate some generalized Sigmoid Beverton-Holt models in time scales, and we obtain the existence and uniqueness of a globally attractive almost periodic solution to the associated dynamic equations with or without survival rates under some suitable assumptions. An example is given to illustrate our abstract results.","PeriodicalId":30985,"journal":{"name":"Nonautonomous Dynamical Systems","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48362871","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
One-dimensional inverse problems of determining the kernel of the integro-differential heat equation in a bounded domain 有界域内积分-微分热方程核确定的一维逆问题
Nonautonomous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.1515/msds-2022-0163
D. Durdiev, J. J. Jumaev
{"title":"One-dimensional inverse problems of determining the kernel of the integro-differential heat equation in a bounded domain","authors":"D. Durdiev, J. J. Jumaev","doi":"10.1515/msds-2022-0163","DOIUrl":"https://doi.org/10.1515/msds-2022-0163","url":null,"abstract":"Abstract The integro-differential equation of heat conduction with the time-convolution integral on the right side is considered. The direct problem is the initial-boundary problem for this integro-differential equation. Two inverse problems are studied for this direct problem consisting in determining a kernel of the integral member on two given additional conditions with respect to the solution of the direct problems, respectively. The problems are replaced with the equivalent system of the integral equations with respect to unknown functions and on the basis of contractive mapping the unique solvability inverse problem.","PeriodicalId":30985,"journal":{"name":"Nonautonomous Dynamical Systems","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42972576","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mathematical analysis of an epidemic model with direct and indirect transmission modes and two delays 具有直接和间接传播模式和两个延迟的流行病模型的数学分析
Nonautonomous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.1515/msds-2023-0103
Fatiha Najm, Radouane Yafia, My Ahmed Aziz Alaoui, Abdessamad Tridane, Lahcen Boukrim
{"title":"Mathematical analysis of an epidemic model with direct and indirect transmission modes and two delays","authors":"Fatiha Najm, Radouane Yafia, My Ahmed Aziz Alaoui, Abdessamad Tridane, Lahcen Boukrim","doi":"10.1515/msds-2023-0103","DOIUrl":"https://doi.org/10.1515/msds-2023-0103","url":null,"abstract":"Abstract In this article, we consider an epidemiological model in which we take into account the effects of direct and indirect transmissions. The first mode occurs through direct contact between infectious and susceptible individuals, and the second one will take place through the shedding of virus particles by infectious individuals and their acquisition by susceptible ones. We also study the effect of latency period and time needed for a susceptible person to become infected by indirect transmission mode. By considering the direct and indirect basic reproduction numbers, we define the basic reproduction number <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mi>R</m:mi> </m:mrow> <m:mrow> <m:mn>0</m:mn> </m:mrow> </m:msub> </m:math> {R}_{0} of the model, which helps us to analyze the stability of equilibria and bifurcation and determine the most sensitive parameters. In conclusion, some numerical simulations are given to confirm the analytical analysis.","PeriodicalId":30985,"journal":{"name":"Nonautonomous Dynamical Systems","volume":"12 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":"135611252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotically almost periodic mild solutions for some partial integrodifferential inclusions using scale of Banach spaces 利用巴拿赫空间的尺度研究部分积分微分包体的渐近概周期温和解
Nonautonomous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.1515/msds-2023-0102
Jaouad El Matloub, Khalil Ezzinbi
{"title":"Asymptotically almost periodic mild solutions for some partial integrodifferential inclusions using scale of Banach spaces","authors":"Jaouad El Matloub, Khalil Ezzinbi","doi":"10.1515/msds-2023-0102","DOIUrl":"https://doi.org/10.1515/msds-2023-0102","url":null,"abstract":"Abstract We are interested in the existence of mild solutions for a class of partial integrodifferential inclusions in infinite dimensional Banach spaces. First, we show the existence of mild solutions with the help of a scale of Banach spaces, the theory of resolvent operators, and the fixed point theory for the measure of non-compactness. Moreover, we examine the existence of asymptotically almost periodic solutions for our problem. Finally, an example of the abstract results is provided.","PeriodicalId":30985,"journal":{"name":"Nonautonomous Dynamical Systems","volume":"16 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":"134890174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mild solution in the α-norm for some partial integrodifferential equations involving a nonlocal condition 一类包含非局部条件的偏积分微分方程的α-范数的温和解
Nonautonomous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.1515/msds-2023-0170
Jaouad El Matloub, K. Ezzinbi
{"title":"Mild solution in the α-norm for some partial integrodifferential equations involving a nonlocal condition","authors":"Jaouad El Matloub, K. Ezzinbi","doi":"10.1515/msds-2023-0170","DOIUrl":"https://doi.org/10.1515/msds-2023-0170","url":null,"abstract":"Abstract In this work, we investigate the existence of mild solutions in the α alpha -norm for a class of nonlocal integrodifferential equations. We employ the theory of resolvent operators introduced by R. Grimmer. The Leray-Schauder alternative is the principal working tool for our analysis.","PeriodicalId":30985,"journal":{"name":"Nonautonomous Dynamical Systems","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44678769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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 of the dynamics of vector-borne diseases transmitted by mosquitoes : taking into account aquatic stages and gonotrophic cycle 蚊子传播媒介传播疾病动态的数学建模：考虑水生阶段和生殖营养周期
Nonautonomous Dynamical Systems Pub Date : 2022-01-01 DOI: 10.1515/msds-2022-0155
Abou Bakari Diabaté, B. Sangaré, Ousmane Koutou
{"title":"Mathematical modeling of the dynamics of vector-borne diseases transmitted by mosquitoes : taking into account aquatic stages and gonotrophic cycle","authors":"Abou Bakari Diabaté, B. Sangaré, Ousmane Koutou","doi":"10.1515/msds-2022-0155","DOIUrl":"https://doi.org/10.1515/msds-2022-0155","url":null,"abstract":"Abstract In this paper, we formulate a mathematical model of vector-borne disease dynamics. The model is constructed by considering two models : a baseline model of vector population dynamics due to Lutambi et al. that takes into account the development of the aquatic stages and the female mosquitoes gonotrophic cycle and an SI-SIR model describing the interaction between mosquitoes and human hosts. We briefly study the baseline model of vectors dynamics and, for the transmission model, we explicitly compute the equilibrium points, and by using the method of Van den Driesshe and J. Watmough, we derive the basic reproduction number ℛ0. Otherwise, thanks to Lyapunov’s principle, Routh-Hurwitz criteria and a favorable result due to Vidyasagar, we establish the local and global stability results of the equilibrium points. Furthermore, we establish an interesting relationship between the mosquito reproduction number ℛv and the basic reproduction number ℛ0. It then follows that aquatic stages and behavior of adult mosquitoes have a significant impact on disease transmission dynamics. Finally, some numerical simulations are carried out to support the theoretical findings of the study.","PeriodicalId":30985,"journal":{"name":"Nonautonomous Dynamical Systems","volume":"9 1","pages":"205 - 236"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46365316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Optimal strategies for controlling the outbreak of COVID-19: Reducing its cost and duration 控制新冠肺炎疫情的最佳策略：降低成本和持续时间
Nonautonomous Dynamical Systems Pub Date : 2022-01-01 DOI: 10.1515/msds-2022-0161
Mohammadali Dashtbali
{"title":"Optimal strategies for controlling the outbreak of COVID-19: Reducing its cost and duration","authors":"Mohammadali Dashtbali","doi":"10.1515/msds-2022-0161","DOIUrl":"https://doi.org/10.1515/msds-2022-0161","url":null,"abstract":"Abstract Social distancing plays an essential role in controlling the spread of an epidemic, but changing the behavior of individuals regarding social distancing is costly. In order to make a rational decision, individuals must compare the cost of social distancing and the cost of infection. People are typically more likely to change their behavior if they are aware that the government is willing to incur additional cost to shorten the duration of an epidemic. I extend an optimal control problem of social distancing by integrating with the SIR model which describes the disease process. I present an optimal control problem to consider the behavior of susceptible individuals and the government in investment as control strategies and compute the equilibrium strategies under the potency of investment, using relative risk functions according to the investment that is made by susceptible individuals and the government. The equilibrium of this problem represents the optimal control strategies for minimizing the cost and duration of controlling an epidemic. Additionally, the model is evaluated using COVID-19 data from Egypt, Japan, Italy, Belgium, Nigeria, and Germany. The findings extracted from this model could be valuable in developing public health policy in the event of an epidemic.","PeriodicalId":30985,"journal":{"name":"Nonautonomous Dynamical Systems","volume":"9 1","pages":"317 - 330"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43072765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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