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Boundary Value Problems最新文献

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Sinc-Galerkin method and a higher-order method for a 1D and 2D time-fractional diffusion equations 一维和二维时间分形扩散方程的 Sinc-Galerkin 方法和高阶方法
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-09-06 DOI: 10.1186/s13661-024-01915-6
Man Luo, Da Xu, Xianmin Pan
{"title":"Sinc-Galerkin method and a higher-order method for a 1D and 2D time-fractional diffusion equations","authors":"Man Luo, Da Xu, Xianmin Pan","doi":"10.1186/s13661-024-01915-6","DOIUrl":"https://doi.org/10.1186/s13661-024-01915-6","url":null,"abstract":"In this article, a new numerical algorithm for solving a 1-dimensional (1D) and 2-dimensional (2D) time-fractional diffusion equation is proposed. The Sinc-Galerkin scheme is considered for spatial discretization, and a higher-order finite difference formula is considered for temporal discretization. The convergence behavior of the methods is analyzed, and the error bounds are provided. The main objective of this paper is to propose the error bounds for 2D problems by using the Sinc-Galerkin method. The proposed method in terms of convergence is studied by using the characteristics of the Sinc function in detail with optimal rates of exponential convergence for 2D problems. Some numerical experiments validate the theoretical results and present the efficiency of the proposed schemes.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"27 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197439","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
Periodic solution for neutral-type differential equation with piecewise impulses on time scales 中性微分方程在时间尺度上的分段脉冲周期解
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-09-04 DOI: 10.1186/s13661-024-01916-5
Chun Peng, Xiaoliang Li, Bo Du
{"title":"Periodic solution for neutral-type differential equation with piecewise impulses on time scales","authors":"Chun Peng, Xiaoliang Li, Bo Du","doi":"10.1186/s13661-024-01916-5","DOIUrl":"https://doi.org/10.1186/s13661-024-01916-5","url":null,"abstract":"In this paper, we establish the existence and stability of periodic solutions for neutral-type differential equations with piecewise impulses on time scales. We first obtain some sufficient conditions for the existence of a unique periodic solution by using the Banach contraction mapping principle. We also prove the existence of at least one periodic solution using the Schauder fixed point theorem. In addition, we establish the stability results based on the existence of periodic solutions. It is worth noting that the results of this paper are based on time scales, so that they are applicable to continuous, discrete, and other types of systems.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"2 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197440","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 multiple birth properties of multi-type Markov branching processes 多类型马尔可夫分支过程的多生特性
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-09-04 DOI: 10.1186/s13661-024-01914-7
Junping Li, Wanting Zhang
{"title":"The multiple birth properties of multi-type Markov branching processes","authors":"Junping Li, Wanting Zhang","doi":"10.1186/s13661-024-01914-7","DOIUrl":"https://doi.org/10.1186/s13661-024-01914-7","url":null,"abstract":"The main purpose of this paper is to consider the multiple birth properties for multi-type Markov branching processes. We first construct a new multi-dimensional Markov process based on the multi-type Markov branching process, which can reveal the multiple birth characteristics. Then the joint probability distribution of multiple birth of multi-type Markov branching process until any time t is obtained by using the new process. Furthermore, the probability distribution of multiple birth until the extinction of the process is also given.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"21 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197438","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
Boundedness of solutions to a second-order periodic system with p-Laplacian and unbounded perturbation terms 具有 p-拉普拉奇和无约束扰动项的二阶周期系统解的有界性
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-08-19 DOI: 10.1186/s13661-024-01911-w
Xiumei Xing, Haiyan Wang, Shaoyong Lai
{"title":"Boundedness of solutions to a second-order periodic system with p-Laplacian and unbounded perturbation terms","authors":"Xiumei Xing, Haiyan Wang, Shaoyong Lai","doi":"10.1186/s13661-024-01911-w","DOIUrl":"https://doi.org/10.1186/s13661-024-01911-w","url":null,"abstract":"The second-order periodic system with p-Laplacian and unbounded time-dependent perturbation terms is investigated. Using the principle integral method, it is shown that under certain assumptions on the unbounded and periodic terms, all solutions to the equation possess boundedness.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"27 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197315","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
Adopted spectral tau approach for the time-fractional diffusion equation via seventh-kind Chebyshev polynomials 通过第七类切比雪夫多项式对时间分量扩散方程采用谱 tau 方法
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-08-16 DOI: 10.1186/s13661-024-01907-6
W. M. Abd-Elhameed, Y. H. Youssri, A. G. Atta
{"title":"Adopted spectral tau approach for the time-fractional diffusion equation via seventh-kind Chebyshev polynomials","authors":"W. M. Abd-Elhameed, Y. H. Youssri, A. G. Atta","doi":"10.1186/s13661-024-01907-6","DOIUrl":"https://doi.org/10.1186/s13661-024-01907-6","url":null,"abstract":"This study utilizes a spectral tau method to acquire an accurate numerical solution of the time-fractional diffusion equation. The central point of this approach is to use double basis functions in terms of certain Chebyshev polynomials, namely Chebyshev polynomials of the seventh-kind and their shifted ones. Some new formulas concerned with these polynomials are derived in this study. A rigorous error analysis of the proposed double expansion further corroborates our research. This analysis is based on establishing some inequalities regarding the selected basis functions. Several numerical examples validate the precision and effectiveness of the suggested method.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"3 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142225221","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
New results on fractional advection–dispersion equations 分数平流-分散方程的新成果
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-08-13 DOI: 10.1186/s13661-024-01910-x
Yan Qiao, Fangqi Chen, Yukun An, Tao Lu
{"title":"New results on fractional advection–dispersion equations","authors":"Yan Qiao, Fangqi Chen, Yukun An, Tao Lu","doi":"10.1186/s13661-024-01910-x","DOIUrl":"https://doi.org/10.1186/s13661-024-01910-x","url":null,"abstract":"In this paper, a class of fractional Sturm–Liouville advection–dispersion equations with instantaneous and noninstantaneous impulses is considered, in particular, the nonlinearities discussed here include Caputo fractional derivatives. Since the nonlinear terms contain fractional derivatives, this problem does not directly have variational structure, we need to combine critical point theory and an iterative method to deal with such problems. Finally, the existence of at least one nontrivial solution is proved by the mountain pass theorem and the iterative method. At the same time, an example is given to illustrate the main result.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"68 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197441","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
Extension of Milne-type inequalities to Katugampola fractional integrals 将米尔恩型不等式扩展到卡图甘波拉分式积分
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-08-13 DOI: 10.1186/s13661-024-01909-4
Abdelghani Lakhdari, Hüseyin Budak, Muhammad Uzair Awan, Badreddine Meftah
{"title":"Extension of Milne-type inequalities to Katugampola fractional integrals","authors":"Abdelghani Lakhdari, Hüseyin Budak, Muhammad Uzair Awan, Badreddine Meftah","doi":"10.1186/s13661-024-01909-4","DOIUrl":"https://doi.org/10.1186/s13661-024-01909-4","url":null,"abstract":"This study explores the extension of Milne-type inequalities to the realm of Katugampola fractional integrals, aiming to broaden the analytical tools available in fractional calculus. By introducing a novel integral identity, we establish a series of Milne-type inequalities for functions possessing extended s-convex first-order derivatives. Subsequently, we present an illustrative example complete with graphical representations to validate our theoretical findings. The paper concludes with practical applications of these inequalities, demonstrating their potential impact across various fields of mathematical and applied sciences.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"32 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197442","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
Nondegeneracy of the solutions for elliptic problem with critical exponent 具有临界指数的椭圆问题解的非遗传性
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-08-07 DOI: 10.1186/s13661-024-01908-5
Qingfang Wang
{"title":"Nondegeneracy of the solutions for elliptic problem with critical exponent","authors":"Qingfang Wang","doi":"10.1186/s13661-024-01908-5","DOIUrl":"https://doi.org/10.1186/s13661-024-01908-5","url":null,"abstract":"This paper deals with the following nonlinear elliptic equation: $$ -Delta u=Q(|y'|,y'')u^{frac{N+2}{N-2}},,,u>0,,,text{in},{ mathbb{R}}^{N},,,uin D^{1,2}({mathbb{R}}^{N}), $$ where $(y',y'')in {mathbb{R}}^{2}times {mathbb{R}}^{N-2}$ , $Ngeq 5$ , $Q(|y'|,y'')$ is a bounded nonnegative function in $mathbb{R}^{2}times {mathbb{R}}^{N-2}$ . By using the local Pohozaev identities we prove a nondegeneracy result for the positive solutions constructed in (Peng et al. in J. Differ. Equ. 267:2503–2530, 2019).","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"105 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933522","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
Bifurcation curve for the Minkowski-curvature equation with concave or geometrically concave nonlinearity 具有凹或几何凹非线性的闵科夫斯基-曲率方程的分岔曲线
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-08-06 DOI: 10.1186/s13661-024-01906-7
Kuo-Chih Hung
{"title":"Bifurcation curve for the Minkowski-curvature equation with concave or geometrically concave nonlinearity","authors":"Kuo-Chih Hung","doi":"10.1186/s13661-024-01906-7","DOIUrl":"https://doi.org/10.1186/s13661-024-01906-7","url":null,"abstract":"We study the bifurcation curve and exact multiplicity of positive solutions in the space $C^{2}left ( (-L,L)right ) cap Cleft ( [-L,L]right ) $ for the Minkowski-curvature equation $$ left { textstylebegin{array}{l} -left ( dfrac{u^{prime }(x)}{sqrt{1-left ( {u^{prime }(x)}right ) ^{2}}}right ) ^{prime }=lambda f(u),text{ }-L< x< L, u(-L)=u(L)=0.end{array}displaystyle right . $$ where $lambda >0$ is a bifurcation parameter, $fin C[0,infty )cap C^{2}(0,infty )$ satisfies $f(u)>0$ for $u>0$ and f is either concave or geometrically concave on $(0,infty )$ . If f is a concave function, we prove that the bifurcation curve is monotone increasing on the $(lambda ,left Vert uright Vert _{infty })$ -plane. If f is a geometrically concave function, we prove that the bifurcation curve is either ⊂-shaped or monotone increasing on the $(lambda ,left Vert uright Vert _{infty })$ -plane under a mild condition. Some interesting applications are given.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"39 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933523","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 p-Laplacian fractional differential equations with nonlocal boundary conditions 一类具有非局部边界条件的 p-Laplacian 分数微分方程正解的存在性
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-08-06 DOI: 10.1186/s13661-024-01905-8
Jiqiang Jiang, Xuelin Sun
{"title":"Existence of positive solutions for a class of p-Laplacian fractional differential equations with nonlocal boundary conditions","authors":"Jiqiang Jiang, Xuelin Sun","doi":"10.1186/s13661-024-01905-8","DOIUrl":"https://doi.org/10.1186/s13661-024-01905-8","url":null,"abstract":"This article is devoted to proving the uniqueness of positive solutions for p-Laplacian equations with Caputo and Riemann-Liouville fractional derivative. The uniqueness result and the dependence of the solution on a parameter are established based on the fixed point point theorem of mixed monotone operators. In the end, a numerical simulation is given to verify the main results.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"34 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933524","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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