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Boundary Value Problems最新文献

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Exploring the solutions of Hilfer delayed Duffing problem on the positive real line 正实线上希尔费延迟杜芬问题解的探索
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-07-30 DOI: 10.1186/s13661-024-01903-w
Sabri T. M. Thabet, Imed Kedim, Thabet Abdeljawad
{"title":"Exploring the solutions of Hilfer delayed Duffing problem on the positive real line","authors":"Sabri T. M. Thabet, Imed Kedim, Thabet Abdeljawad","doi":"10.1186/s13661-024-01903-w","DOIUrl":"https://doi.org/10.1186/s13661-024-01903-w","url":null,"abstract":"In this article, we focus on studying the Duffing problem with the time delay of pantograph type via the Hilfer fractional derivatives on the infinite interval $(0,infty )$ . An appropriate Banach space supported with the Bielecki norm in the Mittag–Leffler function sense is introduced for new and convenient analysis. The existence and uniqueness ( $mathbf{E&U}$ ) of the solutions are proved by utilizing the classical fixed point theorems (FPTs). Moreover, the Hyers–Ulam (HU) stability is discussed for our Hilfer fractional Duffing pantograph system (HFDPS). Ultimately, our results are enhanced by providing numerical examples with graphics simulations to check the validity of the main outcomes.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141870133","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 solvability and boundedness to a attraction–repulsion model with logistic source 具有逻辑源的吸引-排斥模型的全局可解性和有界性
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-07-30 DOI: 10.1186/s13661-024-01904-9
Danqing Zhang
{"title":"Global solvability and boundedness to a attraction–repulsion model with logistic source","authors":"Danqing Zhang","doi":"10.1186/s13661-024-01904-9","DOIUrl":"https://doi.org/10.1186/s13661-024-01904-9","url":null,"abstract":"In this paper, we deal with an attraction–repulsion model with a logistic source as follows: $$begin{aligned} textstylebegin{cases} {u_{t}} = Delta u - chi nabla cdot (u nabla v) + xi nabla cdot (u nabla w) + mu {u^{q}}(1 - u) &text{in } Q , {v_{t}} = Delta v - {alpha _{1}}v + {beta _{1}}u &text{in } Q , {w_{t}} = Delta w - {alpha _{2}}w + {beta _{2}}u & text{in } Q , end{cases}displaystyle end{aligned}$$ where $Q = Omega times {mathbb{R}^{+} }$ , $Omega subset {mathbb{R}^{3}}$ is a bounded domain. We mainly focus on the influence of logistic damping on the global solvability of this model. In dimension 2, q can be equal to 1 (Math. Methods Appl. Sci. 39(2):289–301, 2016). In dimension 3, we derive that the problem admits a global bounded solution when $q>frac{8}{7}$ . In fact, we transfer the difficulty of estimation to the logistic term through iterative methods, thus, compared to the results in (J. Math. Anal. Appl. 2:448 2017; Z. Angew. Math. Phys. 73(2):1–25 2022) in dimension 3, our results do not require any restrictions on the coefficients.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141870134","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
Existence of positive solutions for a class of singular elliptic problems with convection term and critical exponential growth 一类具有对流项和临界指数增长的奇异椭圆问题正解的存在性
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-07-25 DOI: 10.1186/s13661-024-01897-5
Sami Baraket, Anis Ben Ghorbal, Giovany M. Figueiredo
{"title":"Existence of positive solutions for a class of singular elliptic problems with convection term and critical exponential growth","authors":"Sami Baraket, Anis Ben Ghorbal, Giovany M. Figueiredo","doi":"10.1186/s13661-024-01897-5","DOIUrl":"https://doi.org/10.1186/s13661-024-01897-5","url":null,"abstract":"This paper uses the Galerkin method to investigate the existence of positive solution to a class of singular elliptic problems given by $$begin{aligned} textstylebegin{cases} -Delta u= displaystyle frac {lambda _{0}}{u^{beta _{0}}} + Lambda _{0} |nabla u|^{gamma _{0}}+ frac{f_{0}(u)}{|x|^{alpha _{0}}}+ h_{0}(x), u>0 text{in} Omega , u=0 text{on} partial Omega , end{cases}displaystyle end{aligned}$$ where $Omega subset mathbb{R}^{2}$ is a bounded smooth domain, $0<beta _{0}$ , $gamma _{0} leq 1$ , $alpha _{0} in [0,2)$ , $h_{0}(x)geq 0$ , $h_{0}neq 0$ , $h_{0}in L^{infty}(Omega )$ , $0<|h_{0}|_{infty} < lambda _{0} < Lambda _{0}$ , and $f_{0}$ are continuous functions. More precisely, $f_{0}$ has a critical exponential growth, that is, the nonlinearity behaves like $exp (overline{Upsilon}s^{2})$ as $|s| to infty $ , for some $overline{Upsilon}>0$ .","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141786209","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
Existence results for coupled sequential ψ-Hilfer fractional impulsive BVPs: topological degree theory approach 耦合顺序ψ-希尔费分数脉冲 BVPs 的存在结果：拓扑度理论方法
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-07-25 DOI: 10.1186/s13661-024-01901-y
M. Latha Maheswari, K. S. Keerthana Shri, Karthik Muthusamy
{"title":"Existence results for coupled sequential ψ-Hilfer fractional impulsive BVPs: topological degree theory approach","authors":"M. Latha Maheswari, K. S. Keerthana Shri, Karthik Muthusamy","doi":"10.1186/s13661-024-01901-y","DOIUrl":"https://doi.org/10.1186/s13661-024-01901-y","url":null,"abstract":"In this paper, the coupled system of sequential ψ-Hilfer fractional boundary value problems with non-instantaneous impulses is investigated. The existence results of the system are proved by means of topological degree theory. An example is constructed to demonstrate our results. Additionally, a graphical analysis is performed to verify our results.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141786208","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 algorithmic resolution of spectral-element discretization for the time-dependent Stokes problem 时变斯托克斯问题的谱元离散化算法解析
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-07-25 DOI: 10.1186/s13661-024-01900-z
Henda Ouertani, Mohamed Abdelwahed
{"title":"The algorithmic resolution of spectral-element discretization for the time-dependent Stokes problem","authors":"Henda Ouertani, Mohamed Abdelwahed","doi":"10.1186/s13661-024-01900-z","DOIUrl":"https://doi.org/10.1186/s13661-024-01900-z","url":null,"abstract":"We consider two algorithms for the resolution of the time-dependent Stokes problem with nonstandard boundary conditions by the domain-decomposition spectral-element method. The first algorithm (Elimination method) is based on the Uzawa method by decoupling the linear system, while the second algorithm (Global inversion) is based on the overall resolution of the system by the GMRES method. A detailed implementation is proposed and some numerical tests are carried out in two and three dimensions and where the domain is multiply connected.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141779825","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
Effects of Lévy noise and impulsive action on the averaging principle of Atangana–Baleanu fractional stochastic delay differential equations 莱维噪声和脉冲作用对阿坦加纳-巴莱阿努分数随机延迟微分方程平均原理的影响
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-07-25 DOI: 10.1186/s13661-024-01898-4
A. M. Sayed Ahmed, Hamdy M. Ahmed, Karim K. Ahmed, Farah M. Al-Askr, Wael W. Mohammed
{"title":"Effects of Lévy noise and impulsive action on the averaging principle of Atangana–Baleanu fractional stochastic delay differential equations","authors":"A. M. Sayed Ahmed, Hamdy M. Ahmed, Karim K. Ahmed, Farah M. Al-Askr, Wael W. Mohammed","doi":"10.1186/s13661-024-01898-4","DOIUrl":"https://doi.org/10.1186/s13661-024-01898-4","url":null,"abstract":"As delays are common, persistent, and ingrained in daily life, it is imperative to take them into account. In this work, we explore the averaging principle for impulsive Atangana–Baleanu fractional stochastic delay differential equations driven by Lévy noise. The link between the averaged equation solutions and the equivalent solutions of the original equations is shown in the sense of mean square. To achieve the intended outcomes, fractional calculus, semigroup properties, and stochastic analysis theory are used. We also provide an example to demonstrate the practicality and relevance of our research.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141779826","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 solutions of a nonlinear system of q-difference equations 论 q-差分方程非线性系统的解
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-07-25 DOI: 10.1186/s13661-024-01896-6
Nihan Turan, Metin Başarır, Aynur Şahin
{"title":"On the solutions of a nonlinear system of q-difference equations","authors":"Nihan Turan, Metin Başarır, Aynur Şahin","doi":"10.1186/s13661-024-01896-6","DOIUrl":"https://doi.org/10.1186/s13661-024-01896-6","url":null,"abstract":"In this paper, we examine the existence and uniqueness of solutions for a system of the first-order q-difference equations with multi-point and q-integral boundary conditions using various fixed point (fp) theorems. Also, we give two examples to support our results.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141785926","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
Existence of solution of a system of non-linear differential inclusions with non-local, integral boundary conditions via fixed points of hybrid contractions 通过混合收缩的定点求解具有非局部、积分边界条件的非线性微分夹杂系统的存在性
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-07-25 DOI: 10.1186/s13661-024-01902-x
Maliha Rashid, Lariab Shahid, Fatima Dar, Irshad Ayoob, Nabil Mlaiki
{"title":"Existence of solution of a system of non-linear differential inclusions with non-local, integral boundary conditions via fixed points of hybrid contractions","authors":"Maliha Rashid, Lariab Shahid, Fatima Dar, Irshad Ayoob, Nabil Mlaiki","doi":"10.1186/s13661-024-01902-x","DOIUrl":"https://doi.org/10.1186/s13661-024-01902-x","url":null,"abstract":"In the present article, we have introduced the notions of γ-admissibility for the pair of q-ROF set-valued maps and admissible hybrid q-ROF $mathcal{Z}$ -contraction. Notions introduced in the article generalizes the existing concepts in fuzzy literature. Common fixed point result for a pair of γ-admissible q-ROF mappings in b-metric spaces utilizing the introduced contraction is presented. A nontrivial example to support the obtained results is also included. As an application, we have discussed the existence of solution of system of non-linear n-th order differential inclusions with non-local and integral boundary conditions.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141779824","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
Novel analysis of nonlinear seventh-order fractional Kaup–Kupershmidt equation via the Caputo operator 通过卡普托算子对非线性七阶分数考普-库珀施密特方程的新分析
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-07-11 DOI: 10.1186/s13661-024-01895-7
Abdul Hamid Ganie, Saurav Mallik, Mashael M. AlBaidani, Adnan Khan, Mohd Asif Shah
{"title":"Novel analysis of nonlinear seventh-order fractional Kaup–Kupershmidt equation via the Caputo operator","authors":"Abdul Hamid Ganie, Saurav Mallik, Mashael M. AlBaidani, Adnan Khan, Mohd Asif Shah","doi":"10.1186/s13661-024-01895-7","DOIUrl":"https://doi.org/10.1186/s13661-024-01895-7","url":null,"abstract":"In this work, we use two unique methodologies, the homotopy perturbation transform method and Yang transform decomposition method, to solve the fractional nonlinear seventh-order Kaup–Kupershmidt (KK) problem. The physical phenomena that arise in chemistry, physics, and engineering are mathematically explained in this equation, in particular, nonlinear optics, quantum mechanics, plasma physics, fluid dynamics, and so on. The provided methods are used to solve the fractional nonlinear seventh-order KK problem along with the Yang transform and fractional Caputo derivative. The results are significant and necessary for exploring a range of physical processes. This paper uses modern approaches and the fractional operator to develop satisfactory approximations to the offered problem. To solve the fractional KK equation, we first use the Yang transform and fractional Caputo derivative. He’s and Adomian polynomials are useful to manage nonlinear terms. It is shown that the suggested approximate solution converges to the exact one. In these approaches, the results are calculated as convergent series. The key advantage of the recommended approaches is that they provide highly precise results with little computational work. The suggested approach results are compared to the precise solution. By comparing the outcomes with the precise solution using graphs and tables we can verify the efficacy of the offered strategies. Also, the outcomes of the suggested methods at various fractional orders are examined, demonstrating that the findings get more accurate as the value moves from fractional order to integer order. Moreover, the offered methods are innovative, simple, and quite accurate, demonstrating that they are effective for resolving differential equations.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141588001","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
Bitsadze-Samarsky type problems with double involution 带双卷积的比萨泽-萨马尔斯基类型问题
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-07-09 DOI: 10.1186/s13661-024-01892-w
Moldir Muratbekova, Valery Karachik, Batirkhan Turmetov
{"title":"Bitsadze-Samarsky type problems with double involution","authors":"Moldir Muratbekova, Valery Karachik, Batirkhan Turmetov","doi":"10.1186/s13661-024-01892-w","DOIUrl":"https://doi.org/10.1186/s13661-024-01892-w","url":null,"abstract":"In this paper, the solvability of a new class of nonlocal boundary value problems for the Poisson equation is studied. Nonlocal conditions are specified in the form of a connection between the values of the unknown function at different points of the boundary. In this case, the boundary operator is determined using matrices of involution-type mappings. Theorems on the existence and uniqueness of solutions to the studied problems are proved. Using Green’s functions of the classical Dirichlet and Neumann boundary value problems, Green’s functions of the studied problems are constructed and integral representations of solutions to these problems are obtained.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141571775","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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