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Boundary Value Problems最新文献

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A hybrid method to solve a fractional-order Newell–Whitehead–Segel equation 解决分数阶纽厄尔-怀特海-西格尔方程的混合方法
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-03-18 DOI: 10.1186/s13661-023-01795-2
Umut Bektaş, Halil Anaç
{"title":"A hybrid method to solve a fractional-order Newell–Whitehead–Segel equation","authors":"Umut Bektaş, Halil Anaç","doi":"10.1186/s13661-023-01795-2","DOIUrl":"https://doi.org/10.1186/s13661-023-01795-2","url":null,"abstract":"This paper solves fractional differential equations using the Shehu transform in combination with the q-homotopy analysis transform method (q-HATM). As the Shehu transform is only applicable to linear equations, q-HATM is an efficient technique for approximating solutions to nonlinear differential equations. In nonlinear systems that explain the emergence of stripes in 2D systems, the Newell–Whitehead–Segel equation plays a significant role. The findings indicate that the outcomes derived from the tables yield superior results compared to the existing LTDM in the literature. Maple is utilized to depict three-dimensional surfaces and find numerical values that are displayed in a table.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"98 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140153027","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 and multiplicity of solutions for fractional (p_{1}(x,cdot )& p_{2}(x,cdot ))-Laplacian Schrödinger-type equations with Robin boundary conditions 带罗宾边界条件的分数(p_{1}(x,cdot )& p_{2}(x,cdot ))-拉普拉奇薛定谔型方程的解的存在性和多重性
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-03-13 DOI: 10.1186/s13661-024-01844-4
Zhenfeng Zhang, Tianqing An, Weichun Bu, Shuai Li
{"title":"Existence and multiplicity of solutions for fractional (p_{1}(x,cdot )& p_{2}(x,cdot ))-Laplacian Schrödinger-type equations with Robin boundary conditions","authors":"Zhenfeng Zhang, Tianqing An, Weichun Bu, Shuai Li","doi":"10.1186/s13661-024-01844-4","DOIUrl":"https://doi.org/10.1186/s13661-024-01844-4","url":null,"abstract":"In this paper, we study fractional $p_{1}(x,cdot )& p_{2}(x,cdot )$ -Laplacian Schrödinger-type equations for Robin boundary conditions. Under some suitable assumptions, we show that two solutions exist using the mountain pass lemma and Ekeland’s variational principle. Then, the existence of infinitely many solutions is derived by applying the fountain theorem and the Krasnoselskii genus theory, respectively. Different from previous results, the topic of this paper is the Robin boundary conditions in $mathbb{R}^{N}setminus overline{Omega}$ for fractional order $p_{1}(x,cdot )& p_{2}(x,cdot )$ -Laplacian Schrödinger-type equations, including concave-convex nonlinearities, which has not been studied before. In addition, two examples are given to illustrate our results.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"2019 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140126823","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
Blow-up and lifespan of solutions for elastic membrane equation with distributed delay and logarithmic nonlinearity 具有分布式延迟和对数非线性的弹性膜方程解的膨胀和寿命
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-03-08 DOI: 10.1186/s13661-024-01843-5
Salah Boulaaras, Rashid Jan, Abdelbaki Choucha, Aderrahmane Zaraï, Mourad Benzahi
{"title":"Blow-up and lifespan of solutions for elastic membrane equation with distributed delay and logarithmic nonlinearity","authors":"Salah Boulaaras, Rashid Jan, Abdelbaki Choucha, Aderrahmane Zaraï, Mourad Benzahi","doi":"10.1186/s13661-024-01843-5","DOIUrl":"https://doi.org/10.1186/s13661-024-01843-5","url":null,"abstract":"We examine a Kirchhoff-type equation with nonlinear viscoelastic properties, characterized by distributed delay, logarithmic nonlinearity, and Balakrishnan–Taylor damping terms (elastic membrane equation). Under appropriate hypotheses, we establish the occurrence of solution blow-up.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"35 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140076497","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
Caputo fractional backward stochastic differential equations driven by fractional Brownian motion with delayed generator 带延迟发生器的分数布朗运动驱动的卡普托分数后向随机微分方程
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-03-07 DOI: 10.1186/s13661-024-01842-6
Yunze Shao, Junjie Du, Xiaofei Li, Yuru Tan, Jia Song
{"title":"Caputo fractional backward stochastic differential equations driven by fractional Brownian motion with delayed generator","authors":"Yunze Shao, Junjie Du, Xiaofei Li, Yuru Tan, Jia Song","doi":"10.1186/s13661-024-01842-6","DOIUrl":"https://doi.org/10.1186/s13661-024-01842-6","url":null,"abstract":"Over the years, the research of backward stochastic differential equations (BSDEs) has come a long way. As a extension of the BSDEs, the BSDEs with time delay have played a major role in the stochastic optimal control, financial risk, insurance management, pricing, and hedging. In this paper, we study a class of BSDEs with time-delay generators driven by Caputo fractional derivatives. In contrast to conventional BSDEs, in this class of equations, the generator is also affected by the past values of solutions. Under the Lipschitz condition and some new assumptions, we present a theorem on the existence and uniqueness of solutions.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"1 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140054525","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
Positive solutions for a semipositone anisotropic p-Laplacian problem 半正交各向异性 p-Laplacian 问题的正解
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-03-01 DOI: 10.1186/s13661-024-01841-7
A. Razani, Giovany M. Figueiredo
{"title":"Positive solutions for a semipositone anisotropic p-Laplacian problem","authors":"A. Razani, Giovany M. Figueiredo","doi":"10.1186/s13661-024-01841-7","DOIUrl":"https://doi.org/10.1186/s13661-024-01841-7","url":null,"abstract":"In this paper, a semipositone anisotropic p-Laplacian problem $$ -Delta _{overrightarrow{p}}u=lambda f(u), $$ on a bounded domain with the Dirchlet boundary condition is considered, where $A(u^{q}-1)leq f(u)leq B(u^{q}-1)$ for $u>0$ , $f(0)<0$ and $f(u)=0$ for $uleq -1$ . It is proved that there exists $lambda ^{*}>0$ such that if $lambda in (0,lambda ^{*})$ , then the problem has a positive weak solution $u_{lambda}in L^{infty}(overline{Omega})$ via combining Mountain-Pass arguments, comparison principles, and regularity principles.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"5 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140007631","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
Optimal decay-in-time rates of solutions to the Cauchy problem of 3D compressible magneto-micropolar fluids 三维可压缩磁介质流体考奇问题解的最佳时间衰减率
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-02-29 DOI: 10.1186/s13661-024-01839-1
Xinyu Cui, Shengbin Fu, Rui Sun, Fangfang Tian
{"title":"Optimal decay-in-time rates of solutions to the Cauchy problem of 3D compressible magneto-micropolar fluids","authors":"Xinyu Cui, Shengbin Fu, Rui Sun, Fangfang Tian","doi":"10.1186/s13661-024-01839-1","DOIUrl":"https://doi.org/10.1186/s13661-024-01839-1","url":null,"abstract":"This paper focuses on the long time behavior of the solutions to the Cauchy problem of the three-dimensional compressible magneto-micropolar fluids. More precisely, we aim to establish the optimal rates of temporal decay for the highest-order spatial derivatives of the global strong solutions by the method of decomposing frequency. Our result can be regarded as the further investigation of the one in (Wei, Guo and Li in J. Differ. Equ. 263:2457–2480, 2017), in which the authors only provided the optimal rates of temporal decay for the lower-order spatial derivatives of the perturbations of both the velocity and the micro-rotational velocity.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"18 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140007656","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
Generalized strongly n-polynomial convex functions and related inequalities 广义强 n 多项式凸函数及相关不等式
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-02-26 DOI: 10.1186/s13661-024-01838-2
Serap Özcan, Mahir Kadakal, İmdat İşcan, Huriye Kadakal
{"title":"Generalized strongly n-polynomial convex functions and related inequalities","authors":"Serap Özcan, Mahir Kadakal, İmdat İşcan, Huriye Kadakal","doi":"10.1186/s13661-024-01838-2","DOIUrl":"https://doi.org/10.1186/s13661-024-01838-2","url":null,"abstract":"This paper focuses on introducing and examining the class of generalized strongly n-polynomial convex functions. Relationships between these functions and other types of convex functions are explored. The Hermite–Hadamard inequality is established for generalized strongly n-polynomial convex functions. Additionally, new integral inequalities of Hermite–Hadamard type are derived for this class of functions using the Hölder–İşcan integral inequality. The results obtained in this paper are compared with those known in the literature, demonstrating the superiority of the new results. Finally, some applications for special means are provided.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"63 15 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139969721","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
Upper and lower solutions method for a class of second-order coupled systems 一类二阶耦合系统的上下解法
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-02-23 DOI: 10.1186/s13661-024-01837-3
Zelong Yu, Zhanbing Bai, Suiming Shang
{"title":"Upper and lower solutions method for a class of second-order coupled systems","authors":"Zelong Yu, Zhanbing Bai, Suiming Shang","doi":"10.1186/s13661-024-01837-3","DOIUrl":"https://doi.org/10.1186/s13661-024-01837-3","url":null,"abstract":"This paper provides a class of upper and lower solution definitions for second-order coupled systems by transforming the fourth-order differential equation into a second-order differential system. Then, by constructing a homotopy parameter and utilizing the maximum principle, we propose an upper and lower solutions method for studying a class of second-order coupled systems with Dirichlet boundary conditions and obtain an existence result.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"30 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139950813","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
Quasilinear Schrödinger equations with superlinear terms describing the Heisenberg ferromagnetic spin chain 描述海森堡铁磁自旋链的带超线性项的准线性薛定谔方程
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-02-23 DOI: 10.1186/s13661-024-01836-4
Yongkuan Cheng, Yaotian Shen
{"title":"Quasilinear Schrödinger equations with superlinear terms describing the Heisenberg ferromagnetic spin chain","authors":"Yongkuan Cheng, Yaotian Shen","doi":"10.1186/s13661-024-01836-4","DOIUrl":"https://doi.org/10.1186/s13661-024-01836-4","url":null,"abstract":"In this paper, we consider a model problem arising from a classical planar Heisenberg ferromagnetic spin chain: $$ -Delta u+V(x)u-frac{u}{sqrt{1-u^{2}}}Delta sqrt{1-u^{2}}=c vert u vert ^{p-2}u,quad xin mathbb{R}^{N}, $$ where $2< p<2^{*}$ , $c>0$ and $Ngeq 3$ . By the cutoff technique, the change of variables and the $L^{infty}$ estimate, we prove that there exists $c_{0}>0$ , such that for any $c>c_{0}$ this problem admits a positive solution. Here, in contrast to the Morse iteration method, we construct the $L^{infty}$ estimate of the solution. In particular, we give the specific expression of $c_{0}$ .","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"26 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139950811","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 Robin problems for the coupled system of reaction–diffusion equations 反应-扩散方程耦合系统的罗宾问题
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-02-23 DOI: 10.1186/s13661-024-01835-5
Po-Chun Huang, Bo-Yu Pan
{"title":"The Robin problems for the coupled system of reaction–diffusion equations","authors":"Po-Chun Huang, Bo-Yu Pan","doi":"10.1186/s13661-024-01835-5","DOIUrl":"https://doi.org/10.1186/s13661-024-01835-5","url":null,"abstract":"This article investigates the local well-posedness of Turing-type reaction–diffusion equations with Robin boundary conditions in the Sobolev space. Utilizing the Hadamard norm, we derive estimates for Fokas unified transform solutions for linear initial-boundary value problems subject to external forces. Subsequently, we demonstrate that the iteration map, defined by the unified transform solutions and incorporating nonlinearity instead of external forces, acts as a contraction map within an appropriate solution space. Our conclusive result is established through the application of the contraction mapping theorem.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"255 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139950804","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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