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Boundary Value Problems最新文献

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Hybrid cubic and hyperbolic b-spline collocation methods for solving fractional Painlevé and Bagley-Torvik equations in the Conformable, Caputo and Caputo-Fabrizio fractional derivatives 用混合立方和双曲 b-spline 精确定位法求解 Conformable、Caputo 和 Caputo-Fabrizio 分数导数中的 Painlevé 和 Bagley-Torvik 分数方程
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-02-20 DOI: 10.1186/s13661-024-01833-7
Nahid Barzehkar, Reza Jalilian, Ali Barati
{"title":"Hybrid cubic and hyperbolic b-spline collocation methods for solving fractional Painlevé and Bagley-Torvik equations in the Conformable, Caputo and Caputo-Fabrizio fractional derivatives","authors":"Nahid Barzehkar, Reza Jalilian, Ali Barati","doi":"10.1186/s13661-024-01833-7","DOIUrl":"https://doi.org/10.1186/s13661-024-01833-7","url":null,"abstract":"In this paper, we approximate the solution of fractional Painlevé and Bagley-Torvik equations in the Conformable (Co), Caputo (C), and Caputo-Fabrizio (CF) fractional derivatives using hybrid hyperbolic and cubic B-spline collocation methods, which is an extension of the third-degree B-spline function with more smoothness. The hybrid B-spline function is flexible and produces a system of band matrices that can be solved with little computational effort. In this method, three parameters m, η, and λ play an important role in producing accurate results. The proposed methods reduce to the system of linear or nonlinear algebraic equations. The stability and convergence analysis of the methods have been discussed. The numerical examples are presented to illustrate the applications of the methods and compare the computed results with those obtained using other methods.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"4 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139927643","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 of fractional differential equations on infinite intervals 无限区间上分数微分方程解的存在性和多重性
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-02-08 DOI: 10.1186/s13661-024-01832-8
Weichen Zhou, Zhaocai Hao, Martin Bohner
{"title":"Existence and multiplicity of solutions of fractional differential equations on infinite intervals","authors":"Weichen Zhou, Zhaocai Hao, Martin Bohner","doi":"10.1186/s13661-024-01832-8","DOIUrl":"https://doi.org/10.1186/s13661-024-01832-8","url":null,"abstract":"In this research, we investigate the existence and multiplicity of solutions for fractional differential equations on infinite intervals. By using monotone iteration, we identify two solutions, and the multiplicity of solutions is demonstrated by the Leggett–Williams fixed point theorem.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"28 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769576","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 normalized solutions for Schrödinger systems with linear and nonlinear couplings 具有线性和非线性耦合的薛定谔系统的归一化解的存在性
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-02-08 DOI: 10.1186/s13661-024-01830-w
Zhaoyang Yun, Zhitao Zhang
{"title":"Existence of normalized solutions for Schrödinger systems with linear and nonlinear couplings","authors":"Zhaoyang Yun, Zhitao Zhang","doi":"10.1186/s13661-024-01830-w","DOIUrl":"https://doi.org/10.1186/s13661-024-01830-w","url":null,"abstract":"In this paper we study the nonlinear Bose–Einstein condensates Schrödinger system $$ textstylebegin{cases} -Delta u_{1}-lambda _{1} u_{1}=mu _{1} u_{1}^{3}+beta u_{1}u_{2}^{2}+ kappa (x) u_{2}quadtext{in }mathbb{R}^{3}, -Delta u_{2}-lambda _{2} u_{2}=mu _{2} u_{2}^{3}+beta u_{1}^{2}u_{2}+ kappa (x) u_{1}quadtext{in }mathbb{R}^{3}, int _{mathbb{R}^{3}} u_{1}^{2}=a_{1}^{2},qquad int _{mathbb{R}^{3}} u_{2}^{2}=a_{2}^{2}, end{cases} $$ where $a_{1}$ , $a_{2}$ , $mu _{1}$ , $mu _{2}$ , $kappa =kappa (x)>0$ , $beta <0$ , and $lambda _{1}$ , $lambda _{2}$ are Lagrangian multipliers. We use the Ekeland variational principle and the minimax method on manifold to prove that this system has a solution that is radially symmetric and positive.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"15 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769797","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
Infinitely many solutions for quasilinear Schrödinger equation with concave-convex nonlinearities 具有凹凸非线性的准线性薛定谔方程的无限多解
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-02-06 DOI: 10.1186/s13661-023-01805-3
Lijuan Chen, Caisheng Chen, Qiang Chen, Yunfeng Wei
{"title":"Infinitely many solutions for quasilinear Schrödinger equation with concave-convex nonlinearities","authors":"Lijuan Chen, Caisheng Chen, Qiang Chen, Yunfeng Wei","doi":"10.1186/s13661-023-01805-3","DOIUrl":"https://doi.org/10.1186/s13661-023-01805-3","url":null,"abstract":"In this work, we study the existence of infinitely many solutions to the following quasilinear Schrödinger equations with a parameter α and a concave-convex nonlinearity: 0.1 $$begin{aligned}& -Delta _{p}u+V(x) vert u vert ^{p-2}u-Delta _{p}bigl( vert u vert ^{2alpha}bigr) vert u vert ^{2alpha -2}u= lambda h_{1}(x) vert u vert ^{m-2}u+h_{2}(x) vert u vert ^{q-2}u, & quad xin {mathbb{R}}^{N}, end{aligned}$$ where $Delta _{p}u=operatorname{div}(|nabla u|^{p-2}nabla u)$ , $1< p< N$ , $lambda ge 0$ , and $1< m< p<2alpha p<q<2alpha p^{*}=frac{2alpha pN}{N-p}$ . The functions $V(x)$ , $h_{1}(x)$ , and $h_{2}(x)$ satisfy some suitable conditions. Using variational methods and some special techniques, we prove that there exists $lambda _{0}>0$ such that Eq. (0.1) admits infinitely many high energy solutions in $W^{1,p}({mathbb{R}}^{N})$ provided that $lambda in [0,lambda _{0}]$ .","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"23 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769759","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
Infinite system of nonlinear tempered fractional order BVPs in tempered sequence spaces 钢化序列空间中的非线性钢化分数阶 BVP 无限系统
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-02-01 DOI: 10.1186/s13661-024-01826-6
Sabbavarapu Nageswara Rao, Mahammad Khuddush, Ahmed Hussein Msmali, Abdullah Ali H. Ahmadini
{"title":"Infinite system of nonlinear tempered fractional order BVPs in tempered sequence spaces","authors":"Sabbavarapu Nageswara Rao, Mahammad Khuddush, Ahmed Hussein Msmali, Abdullah Ali H. Ahmadini","doi":"10.1186/s13661-024-01826-6","DOIUrl":"https://doi.org/10.1186/s13661-024-01826-6","url":null,"abstract":"This paper deals with the existence results of the infinite system of tempered fractional BVPs $$begin{aligned}& {}^{mathtt{R}}_{0}mathrm{D}_{mathrm{r}}^{varrho , uplambda} mathtt{z}_{mathtt{j}}(mathrm{r})+psi _{mathtt{j}}bigl(mathrm{r}, mathtt{z}(mathrm{r})bigr)=0,quad 0< mathrm{r}< 1, & mathtt{z}_{mathtt{j}}(0)=0,qquad {}^{mathtt{R}}_{0} mathrm{D}_{ mathrm{r}}^{mathtt{m}, uplambda} mathtt{z}_{mathtt{j}}(0)=0, & mathtt{b}_{1} mathtt{z}_{mathtt{j}}(1)+mathtt{b}_{2} {}^{ mathtt{R}}_{0}mathrm{D}_{mathrm{r}}^{mathtt{m}, uplambda} mathtt{z}_{mathtt{j}}(1)=0, end{aligned}$$ where $mathtt{j}in mathbb{N}$ , $2<varrho le 3$ , $1<mathtt{m}le 2$ , by utilizing the Hausdorff measure of noncompactness and Meir–Keeler fixed point theorem in a tempered sequence space.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"292 1 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139657811","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
Nonexistence of positive solutions for the weighted higher-order elliptic system with Navier boundary condition 带纳维边界条件的加权高阶椭圆系统正解的不存在性
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-01-26 DOI: 10.1186/s13661-024-01831-9
Weiwei Zhao, Xiaoling Shao, Changhui Hu, Zhiyu Cheng
{"title":"Nonexistence of positive solutions for the weighted higher-order elliptic system with Navier boundary condition","authors":"Weiwei Zhao, Xiaoling Shao, Changhui Hu, Zhiyu Cheng","doi":"10.1186/s13661-024-01831-9","DOIUrl":"https://doi.org/10.1186/s13661-024-01831-9","url":null,"abstract":"We establish a Liouville-type theorem for a weighted higher-order elliptic system in a wider exponent region described via a critical curve. We first establish a Liouville-type theorem to the involved integral system and then prove the equivalence between the two systems by using superharmonic properties of the differential systems. This improves the results in (Complex Var. Elliptic Equ. 5:1436–1450, 2013) and (Abstr. Appl. Anal. 2014:593210, 2014).","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"34 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139582786","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 solutions for a 4-dimensional semilinear elliptic system of Liouville type in some general cases 柳维尔型四维半线性椭圆系统在某些一般情况下的膨胀解
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-01-25 DOI: 10.1186/s13661-024-01828-4
Sami Baraket, Anis Ben Ghorbal, Rima Chetouane, Azedine Grine
{"title":"Blow-up solutions for a 4-dimensional semilinear elliptic system of Liouville type in some general cases","authors":"Sami Baraket, Anis Ben Ghorbal, Rima Chetouane, Azedine Grine","doi":"10.1186/s13661-024-01828-4","DOIUrl":"https://doi.org/10.1186/s13661-024-01828-4","url":null,"abstract":"This paper is devoted to the existence of singular limit solutions for a nonlinear elliptic system of Liouville type under Navier boundary conditions in a bounded open domain of $mathbb{R}^{4}$ . The concerned results are obtained employing the nonlinear domain decomposition method and a Pohozaev-type identity.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"12 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139582914","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
Least energy nodal solutions for a weighted ((N, p))-Schrödinger problem involving a continuous potential under exponential growth nonlinearity 指数增长非线性条件下涉及连续势的加（(N, p)）权薛定谔问题的最小能量节点解
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-01-25 DOI: 10.1186/s13661-024-01829-3
Sami Baraket, Brahim Dridi, Azedine Grine, Rached Jaidane
{"title":"Least energy nodal solutions for a weighted ((N, p))-Schrödinger problem involving a continuous potential under exponential growth nonlinearity","authors":"Sami Baraket, Brahim Dridi, Azedine Grine, Rached Jaidane","doi":"10.1186/s13661-024-01829-3","DOIUrl":"https://doi.org/10.1186/s13661-024-01829-3","url":null,"abstract":"This article aims to investigate the existence of nontrivial solutions with minimal energy for a logarithmic weighted $(N,p)$ -Laplacian problem in the unit ball B of $mathbb{R}^{N}$ , $N>2$ . The nonlinearities of the equation are critical or subcritical growth, which is motivated by weighted Trudinger–Moser type inequalities. Our approach is based on constrained minimization within the Nehari set, the quantitative deformation lemma, and degree theory results.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"101 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139560725","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 type of the unique continuation property for a fractional diffusion equation and an inverse source problem 分式扩散方程和反源问题的新型唯一延续特性
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-01-23 DOI: 10.1186/s13661-024-01827-5
Wenyi Liu, Chengbin Du, Zhiyuan Li
{"title":"New type of the unique continuation property for a fractional diffusion equation and an inverse source problem","authors":"Wenyi Liu, Chengbin Du, Zhiyuan Li","doi":"10.1186/s13661-024-01827-5","DOIUrl":"https://doi.org/10.1186/s13661-024-01827-5","url":null,"abstract":"In this work, a new type of the unique continuation property for time-fractional diffusion equations is studied. The proof is mainly based on the Laplace transform and the properties of Bessel functions. As an application, the uniqueness of the inverse problem in the simultaneous determination of spatially dependent source terms and fractional order from sparse boundary observation data is established.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"60 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139560541","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
A necessary and sufficient condition for the existence of global solutions to reaction-diffusion equations on bounded domains 有界域上反应扩散方程全局解存在的必要条件和充分条件
IF 1.7 4区 数学
Boundary Value Problems Pub Date : 2024-01-22 DOI: 10.1186/s13661-024-01822-w
Soon-Yeong Chung, Jaeho Hwang
{"title":"A necessary and sufficient condition for the existence of global solutions to reaction-diffusion equations on bounded domains","authors":"Soon-Yeong Chung, Jaeho Hwang","doi":"10.1186/s13661-024-01822-w","DOIUrl":"https://doi.org/10.1186/s13661-024-01822-w","url":null,"abstract":"The purpose of this paper is to give a necessary and sufficient condition for the existence and non-existence of global solutions of the following semilinear parabolic equations $$ u_{t}=Delta u+psi (t)f(u),quad text{in }Omega times (0,infty ), $$ under the mixed boundary condition on a bounded domain Ω. In fact, this has remained an open problem for a few decades, even for the case $f(u)=u^{p}$ . As a matter of fact, we prove: $$ begin{aligned} & text{there is no global solution for any initial data if and only if } & int _{0}^{infty}psi (t) frac{f (lVert S(t)u_{0}rVert _{infty} )}{lVert S(t)u_{0}rVert _{infty}},dt= infty &text{for every nonnegative nontrivial initial data } u_{0}in C_{0}( Omega ). end{aligned} $$ Here, $(S(t))_{tgeq 0}$ is the heat semigroup with the mixed boundary condition.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"4 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139518434","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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