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Advances in Differential Equations最新文献

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High and low perturbations of the critical Choquard equation on the Heisenberg group 海森堡群上临界乔卡方程的高扰动和低扰动
IF 1.4 3区 数学
Advances in Differential Equations Pub Date : 2023-10-20 DOI: 10.57262/ade029-0304-153
Shujie Bai, Yueqiang Song, Duvsan D. Repovvs
{"title":"High and low perturbations of the critical Choquard equation on the Heisenberg group","authors":"Shujie Bai, Yueqiang Song, Duvsan D. Repovvs","doi":"10.57262/ade029-0304-153","DOIUrl":"https://doi.org/10.57262/ade029-0304-153","url":null,"abstract":"We study the following critical Choquard equation on the Heisenberg group: begin{equation*} begin{cases} displaystyle {-Delta_H u }={mu} |u|^{q-2}u+int_{Omega} frac{|u(eta)|^{Q_{lambda}^{ast}}} {|eta^{-1}xi|^{lambda}} deta|u|^{Q_{lambda}^{ast}-2}u&mbox{in } Omega, u=0&mbox{on } partialOmega, end{cases} end{equation*} where $Omegasubset mathbb{H}^N$ is a smooth bounded domain, $Delta_H$ is the Kohn-Laplacian on the Heisenberg group $mathbb{H}^N$, $1<q<2$ or $2<q<Q_lambda^ast$, $mu>0$, $0<lambda<Q=2N+2$, and $Q_{lambda}^{ast}=frac{2Q-lambda}{Q-2}$ is the critical exponent. Using the concentration compactness principle and the critical point theory, we prove that the above problem has the least two positive solutions for $1<q<2$ in the case of low perturbations (small values of $mu$), and has a nontrivial solution for $2<q<Q_lambda^ast$ in the case of high perturbations (large values of $mu$). Moreover, for $1<q<2$, we also show that there is a positive ground state solution, and for $2<q<Q_lambda^ast$, there are at least $n$ pairs of nontrivial weak solutions.","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139316049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 Helmholtz decomposition of a $BMO$ type vector field in general unbounded domains 一般无界域中 $BMO$ 类型向量场的赫尔姆霍兹分解
IF 1.4 3区 数学
Advances in Differential Equations Pub Date : 2023-07-19 DOI: 10.57262/ade029-0506-389
Y. Giga, Zhongyang Gu
{"title":"The Helmholtz decomposition of a $BMO$ type vector field in general unbounded domains","authors":"Y. Giga, Zhongyang Gu","doi":"10.57262/ade029-0506-389","DOIUrl":"https://doi.org/10.57262/ade029-0506-389","url":null,"abstract":"We consider a space of $L^2$ vector fields with bounded mean oscillation whose ``normal'' component to the boundary is well-controlled. In the case when the dimension $n geq 3$, we establish its Helmholtz decomposition for arbitrary uniformly $C^3$ domain in $mathbf{R}^n$.","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139357574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Impulsive evolution processes: abstract results and an application to a coupled wave equations 脉冲演化过程：抽象结果及其在耦合波动方程中的应用
IF 1.4 3区 数学
Advances in Differential Equations Pub Date : 2023-07-01 DOI: 10.57262/ade028-0708-569
E. Bonotto, M. J. Nascimento, E. B. Santiago
{"title":"Impulsive evolution processes: abstract results and an application to a coupled wave equations","authors":"E. Bonotto, M. J. Nascimento, E. B. Santiago","doi":"10.57262/ade028-0708-569","DOIUrl":"https://doi.org/10.57262/ade028-0708-569","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44504620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 1
Multiplicity results of solutions to the double phase anisotropic variational problems involving variable exponent 涉及变指数的双相各向异性变分问题解的多重性结果
IF 1.4 3区 数学
Advances in Differential Equations Pub Date : 2023-05-01 DOI: 10.57262/ade028-0506-467
Jinxia Cen, Seon-Jin Kim, Yun-Ho Kim, Shengda Zeng
{"title":"Multiplicity results of solutions to the double phase anisotropic variational problems involving variable exponent","authors":"Jinxia Cen, Seon-Jin Kim, Yun-Ho Kim, Shengda Zeng","doi":"10.57262/ade028-0506-467","DOIUrl":"https://doi.org/10.57262/ade028-0506-467","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46271721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 3
Hierarchical exact controllability of hyperbolic equations and Dunford-Pettis' theorem 双曲方程的层次精确可控性及Dunford-Pettis定理
IF 1.4 3区 数学
Advances in Differential Equations Pub Date : 2023-05-01 DOI: 10.57262/ade028-0506-505
F. D. Araruna, E. Fernández-Cara, L. C. da Silva
{"title":"Hierarchical exact controllability of hyperbolic equations and Dunford-Pettis' theorem","authors":"F. D. Araruna, E. Fernández-Cara, L. C. da Silva","doi":"10.57262/ade028-0506-505","DOIUrl":"https://doi.org/10.57262/ade028-0506-505","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46678933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 solution for a class of elliptic problems with indefinite nonlinearities with critical and supercritical growth 一类具有临界和超临界增长的不定非线性椭圆问题正解的存在性
IF 1.4 3区 数学
Advances in Differential Equations Pub Date : 2023-05-01 DOI: 10.57262/ade028-0506-347
G. Costa, G. Figueiredo, J. C. Junior
{"title":"Existence of positive solution for a class of elliptic problems with indefinite nonlinearities with critical and supercritical growth","authors":"G. Costa, G. Figueiredo, J. C. Junior","doi":"10.57262/ade028-0506-347","DOIUrl":"https://doi.org/10.57262/ade028-0506-347","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47975834","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 2
Multiple positive bound state solutions for fractional Schrödinger-Poisson system with critical growth 临界生长分数阶Schrödinger-Poisson系统的多重正界态解
IF 1.4 3区 数学
Advances in Differential Equations Pub Date : 2023-03-01 DOI: 10.57262/ade028-0304-217
Wen Guan, Da-Bin Wang
{"title":"Multiple positive bound state solutions for fractional Schrödinger-Poisson system with critical growth","authors":"Wen Guan, Da-Bin Wang","doi":"10.57262/ade028-0304-217","DOIUrl":"https://doi.org/10.57262/ade028-0304-217","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44251240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Landesman-Lazer type conditions for scalar one-sided superlinear nonlinearities with Neumann boundary conditions 具有Neumann边界条件的标量单边超线性非线性的Landesman-Lazer型条件
IF 1.4 3区 数学
Advances in Differential Equations Pub Date : 2023-03-01 DOI: 10.57262/ade028-0304-247
Rossella Marvulli, Andrea Sfecci
{"title":"Landesman-Lazer type conditions for scalar one-sided superlinear nonlinearities with Neumann boundary conditions","authors":"Rossella Marvulli, Andrea Sfecci","doi":"10.57262/ade028-0304-247","DOIUrl":"https://doi.org/10.57262/ade028-0304-247","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46752692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Critical problems with Hardy potential on Stratified Lie Groups 分层李群上Hardy势的临界问题
IF 1.4 3区 数学
Advances in Differential Equations Pub Date : 2023-01-01 DOI: 10.57262/ade028-0102-1
Annunziata Loiudice
{"title":"Critical problems with Hardy potential on Stratified Lie Groups","authors":"Annunziata Loiudice","doi":"10.57262/ade028-0102-1","DOIUrl":"https://doi.org/10.57262/ade028-0102-1","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45418728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 2
Double-wall carbon nanotubes model with nonlinear localized damping: Asymptotic stability 具有非线性局域阻尼的双壁碳纳米管模型:渐近稳定性
IF 1.4 3区 数学
Advances in Differential Equations Pub Date : 2023-01-01 DOI: 10.57262/ade028-0910-753
M.L. Santos, D. S. Almeida Júnior, S. Cordeiro, R. Lobato
{"title":"Double-wall carbon nanotubes model with nonlinear localized damping: Asymptotic stability","authors":"M.L. Santos, D. S. Almeida Júnior, S. Cordeiro, R. Lobato","doi":"10.57262/ade028-0910-753","DOIUrl":"https://doi.org/10.57262/ade028-0910-753","url":null,"abstract":"","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71111712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 1
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