Pub Date : 2024-07-30DOI: 10.1186/s13661-024-01903-w
Sabri T. M. Thabet, Imed Kedim, Thabet Abdeljawad
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.
{"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}
Pub Date : 2024-07-30DOI: 10.1186/s13661-024-01904-9
Danqing Zhang
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.
在本文中，我们将讨论一个具有逻辑源的吸引-排斥模型，具体如下：$$begin{aligned}contextstylebegin{cases}{u_{t}} = Delta u - chi nabla cdot (u nabla v) + xi nabla cdot (u nabla w) + mu {u^{q}}(1 - u) &text{in }Q , {v_{t}} = Delta v - {alpha _{1}}v + {beta _{1}}u &text{in }Q , {w_{t}} = Delta w - {alpha _{2}}w + {beta _{2}}u & （text{in }Q , end{cases}displaystyle end{aligned}$$ 其中 $Q = Omega times {mathbb{R}^{+} }$ , $Omega subset {mathbb{R}^{3}}$ 是一个有界域。我们主要关注逻辑阻尼对该模型全局可解性的影响。在维度 2 中，q 可以等于 1（Math.方法应用科学》39(2):289-301, 2016）。在维度 3 中，我们推导出当 $q>frac{8}{7}$ 时，该问题存在全局有界解。 事实上，我们通过迭代法将估计难度转移到了逻辑项上，因此，与《数学分析》（J. Math. Anal.Anal.Appl. 2:448 2017; Z. Angew.Math.Phys. 73(2):1-25 2022）在维 3 中的结果相比，我们的结果不需要对系数进行任何限制。
{"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}
Pub Date : 2024-07-25DOI: 10.1186/s13661-024-01897-5
Sami Baraket, Anis Ben Ghorbal, Giovany M. Figueiredo
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, $00$ .
{"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}
Pub Date : 2024-07-25DOI: 10.1186/s13661-024-01901-y
M. Latha Maheswari, K. S. Keerthana Shri, Karthik Muthusamy
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.
{"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}
Pub Date : 2024-07-25DOI: 10.1186/s13661-024-01900-z
Henda Ouertani, Mohamed Abdelwahed
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.
{"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}
Pub Date : 2024-07-25DOI: 10.1186/s13661-024-01898-4
A. M. Sayed Ahmed, Hamdy M. Ahmed, Karim K. Ahmed, Farah M. Al-Askr, Wael W. Mohammed
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.
{"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}
Pub Date : 2024-07-25DOI: 10.1186/s13661-024-01896-6
Nihan Turan, Metin Başarır, Aynur Şahin
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.
{"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}
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.
{"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}
Pub Date : 2024-07-11DOI: 10.1186/s13661-024-01895-7
Abdul Hamid Ganie, Saurav Mallik, Mashael M. AlBaidani, Adnan Khan, Mohd Asif Shah
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.
在这项工作中，我们采用同调扰动变换法和杨变换分解法这两种独特的方法来求解分数非线性七阶 Kaup-Kupershmidt (KK) 问题。化学、物理学和工程学中出现的物理现象都可以用这个方程进行数学解释，特别是非线性光学、量子力学、等离子体物理学、流体动力学等。所提供的方法用于解决分数非线性七阶 KK 问题以及杨变换和分数卡普托导数。这些结果对于探索一系列物理过程具有重要意义和必要性。本文利用现代方法和分数算子对所提供的问题进行了令人满意的近似。为了求解分数 KK 方程，我们首先使用了杨变换和分数卡普托导数。He's 和 Adomian 多项式可用于管理非线性项。结果表明，建议的近似解收敛于精确解。在这些方法中，计算结果都是收敛级数。推荐方法的主要优点是只需很少的计算量就能得到非常精确的结果。建议方法的结果会与精确解进行比较。通过使用图形和表格将结果与精确解进行比较，我们可以验证所提供策略的有效性。此外，我们还研究了所建议方法在不同小数阶的结果，结果表明，随着数值从小数阶移动到整数阶，结果会变得更加精确。此外，所提供的方法新颖、简单且相当精确，表明它们在解决微分方程方面非常有效。
{"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}
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.
{"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}
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