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Infinitely Many Solutions for the Fractional Nonlinear Schrödinger Equations of a New Type 一类新型分数阶非线性Schrödinger方程的无穷多解
IF 0.3 4区 数学
Journal of Partial Differential Equations Pub Date : 2022-06-01 DOI: 10.4208/jpde.v35.n3.5
Qing Guo null, Lixiu Duan
{"title":"Infinitely Many Solutions for the Fractional Nonlinear Schrödinger Equations of a New Type","authors":"Qing Guo null, Lixiu Duan","doi":"10.4208/jpde.v35.n3.5","DOIUrl":"https://doi.org/10.4208/jpde.v35.n3.5","url":null,"abstract":". This paper, we study the multiplicity of solutions for the fractional Schr¨odinger equation with s ∈ ( 0,1 ) , N ≥ 3, p ∈ ( 1, 2 N N − 2 s − 1 ) and lim | y |→ + ∞ V ( y ) > 0. By assuming suitable decay property of the radial potential V ( y ) = V ( | y | ) , we construct another type of solutions concentrating at infinite vertices of two similar equilateral polygonal with infinitely large length of sides. Hence, besides the length of each polygonal, we must consider one more parameter, that is the height of the podetium, simultaneously. Another difficulty lies in the non-local property of the operator ( − ∆ ) s and the algebraic decay involving the approximation solutions make the estimates become more subtle.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83973831","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 Singular Moser-Trudinger Inequality on Metric Measure Space 度量测度空间上的一个奇异Moser-Trudinger不等式
IF 0.3 4区 数学
Journal of Partial Differential Equations Pub Date : 2022-06-01 DOI: 10.4208/jpde.v35.n4.3
Yaoting Gui
{"title":"A Singular Moser-Trudinger Inequality on Metric Measure Space","authors":"Yaoting Gui","doi":"10.4208/jpde.v35.n4.3","DOIUrl":"https://doi.org/10.4208/jpde.v35.n4.3","url":null,"abstract":". Let ( X , d , µ ) be a metric space with a Borel-measure µ , suppose µ satisfies the Ahlfors-regular condition, i.e. where b 1 , b 2 are two positive constants and s is the volume growth exponent. In this paper, we mainly study two things, one is to consider the best constant of the Moser-Trudinger inequality on such metric space under the condition that s is not less than 2. The other is to study the generalized Moser-Trudinger inequality with a singular weight.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86043312","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
Mean Field Equations for the Equilibrium Turbulence and Toda Systems on Connected Finite Graphs 有限连通图上平衡湍流和Toda系统的平均场方程
IF 0.3 4区 数学
Journal of Partial Differential Equations Pub Date : 2022-06-01 DOI: 10.4208/jpde.v35.n3.1
Xiao-Dan Zhu
{"title":"Mean Field Equations for the Equilibrium Turbulence and Toda Systems on Connected Finite Graphs","authors":"Xiao-Dan Zhu","doi":"10.4208/jpde.v35.n3.1","DOIUrl":"https://doi.org/10.4208/jpde.v35.n3.1","url":null,"abstract":". In this paper, we study existence of solutions of mean field equations for the equilibrium turbulence and Toda systems on connected finite graphs. Our method is based on calculus of variations, which was built on connected finite graphs by Grigor’yan, Lin and Yang.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74446690","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: 5
Global Well-Posedness of Solutions to 2D Prandtl-Hartmann Equations in Analytic Framework 解析框架下二维Prandtl-Hartmann方程解的全局适定性
IF 0.3 4区 数学
Journal of Partial Differential Equations Pub Date : 2022-06-01 DOI: 10.4208/jpde.v35.n3.7
Xiaolei Dong null, Yuming Qin
{"title":"Global Well-Posedness of Solutions to 2D Prandtl-Hartmann Equations in Analytic Framework","authors":"Xiaolei Dong null, Yuming Qin","doi":"10.4208/jpde.v35.n3.7","DOIUrl":"https://doi.org/10.4208/jpde.v35.n3.7","url":null,"abstract":". In this paper, we consider the two-dimensional (2D) Prandtl-Hartmann equations on the half plane and prove the global existence and uniqueness of solutions to 2D Prandtl-Hartmann equations by using the classical energy methods in analytic framework. We prove that the lifespan of the solutions to 2D Prandtl-Hartmann equations can be extended up to T ε (see Theorem 2.1) when the strength of the perturbation is of the order of ε . The difficulty of solving the Prandtl-Hartmann equations in the analytic framework is the loss of x -derivative in the term v ∂ y u . To overcome this difficulty, we introduce the Gaussian weighted Poincar´ e inequality (see Lemma 2.3). Com-pared to the existence and uniqueness of solutions to the classical Prandtl equations where the monotonicity condition of the tangential velocity plays a key role, which is not needed for the 2D Prandtl-Hartmann equations in analytic framework. Besides, the existence and uniqueness of solutions to the 2D MHD boundary layer where the initial tangential magnetic field has a lower bound plays an important role, which is not needed for the 2D Prandtl-Hartmann equations in analytic framework, either.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74810291","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: 2
Global Well-Posedness for the 3D Tropical Climate Model without Thermal Diffusion 无热扩散的三维热带气候模式的全球适定性
IF 0.3 4区 数学
Journal of Partial Differential Equations Pub Date : 2022-06-01 DOI: 10.4208/jpde.v35.n4.4
Yanghai Yu, Jinlu Li null, Xiuwei Yin
{"title":"Global Well-Posedness for the 3D Tropical Climate Model without Thermal Diffusion","authors":"Yanghai Yu, Jinlu Li null, Xiuwei Yin","doi":"10.4208/jpde.v35.n4.4","DOIUrl":"https://doi.org/10.4208/jpde.v35.n4.4","url":null,"abstract":". In this paper, we consider the Cauchy problem of 3D tropical climate model with zero thermal diffusion. Firstly, we establish the global regularity for this system with fractional diffusion α = β = 5/4. Secondly, by adding only a damp term, we obtain the global well-posedness for small initial data.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89539675","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
Doubly Nonlinear Degenerate Parabolic Equations with a Singular Potential for Greiner Vector Fields 具有奇异势的双非线性退化抛物方程
IF 0.3 4区 数学
Journal of Partial Differential Equations Pub Date : 2022-06-01 DOI: 10.4208/jpde.v35.n4.1
Junqiang Han
{"title":"Doubly Nonlinear Degenerate Parabolic Equations with a Singular Potential for Greiner Vector Fields","authors":"Junqiang Han","doi":"10.4208/jpde.v35.n4.1","DOIUrl":"https://doi.org/10.4208/jpde.v35.n4.1","url":null,"abstract":". The purpose of this paper is to investigate the nonexistence of positive solutions of the following doubly nonlinear degenerate parabolic equations: where Ω is a Carnot-Carath´eodory metric ball in R 2 n + 1 generated by Greiner vector fields, V ∈ L 1 loc ( Ω ) , k ∈ N , m ∈ R , 1 < p < 2 n + 2 k and m + p − 2 > 0. The better lower bound p ∗ for m + p is found and the nonexistence results are proved for p ∗ 6 m + p < 3.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72821918","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
Global Integrability for Solutions to Obstacle Problems 障碍问题解的全局可积性
IF 0.3 4区 数学
Journal of Partial Differential Equations Pub Date : 2022-06-01 DOI: 10.4208/jpde.v35.n4.2
Yanan Shan null, Hongya Gao
{"title":"Global Integrability for Solutions to Obstacle Problems","authors":"Yanan Shan null, Hongya Gao","doi":"10.4208/jpde.v35.n4.2","DOIUrl":"https://doi.org/10.4208/jpde.v35.n4.2","url":null,"abstract":". Denote v ≥ ψ , a.e. and v − θ p Ω ) o where ψ is any function in Ω ⊂ R N , N ≥ 2, with values in R ∪{± ∞ } and θ is a measurable function. This paper deals with global integrability for u ∈K ψ , θ such that with |A ( x , ξ ) |≈| ξ | p − 1 , 1 < p < N . Some global integrability results are obtained.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81596895","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 Obstacle Problem For Nonlinear Degenerate Elliptic Equations with Variable Exponents and L$^1$-Data 具有L$^1$-数据的变指数非线性退化椭圆方程的障碍问题
IF 0.3 4区 数学
Journal of Partial Differential Equations Pub Date : 2022-06-01 DOI: 10.4208/jpde.v35.n2.1
H. Khelifi
{"title":"The Obstacle Problem For Nonlinear Degenerate Elliptic Equations with Variable Exponents and L$^1$-Data","authors":"H. Khelifi","doi":"10.4208/jpde.v35.n2.1","DOIUrl":"https://doi.org/10.4208/jpde.v35.n2.1","url":null,"abstract":"","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91218907","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
Asymptotic Behavior of Solutions for the Porous Media Equations with Nonlinear Norm-type Sources 具有非线性范数型源的多孔介质方程解的渐近行为
IF 0.3 4区 数学
Journal of Partial Differential Equations Pub Date : 2022-06-01 DOI: 10.4208/jpde.v35.n3.4
Yingzhen Xue
{"title":"Asymptotic Behavior of Solutions for the Porous Media Equations with Nonlinear Norm-type Sources","authors":"Yingzhen Xue","doi":"10.4208/jpde.v35.n3.4","DOIUrl":"https://doi.org/10.4208/jpde.v35.n3.4","url":null,"abstract":"","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91302621","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
Serrin-Type Overdetermined Problem in $mathbb H^n$ $mathbb H^n$中的serrin型超定问题
IF 0.3 4区 数学
Journal of Partial Differential Equations Pub Date : 2022-01-12 DOI: 10.4208/jpde.v36.n1.7
Zhenghuan Gao, Xiaohan Jia, Jingquan Yan
{"title":"Serrin-Type Overdetermined Problem in $mathbb H^n$","authors":"Zhenghuan Gao, Xiaohan Jia, Jingquan Yan","doi":"10.4208/jpde.v36.n1.7","DOIUrl":"https://doi.org/10.4208/jpde.v36.n1.7","url":null,"abstract":"In this paper, we prove the symmetry of the solution to overdetermined problem for the equation σk(D 2 u − uI) = C n in hyperbolic space. Our approach is based on establishing a RellichPohozaev type identity and using a P function. Our result generalizes the overdetermined problem for Hessian equation in Euclidean space.","PeriodicalId":43504,"journal":{"name":"Journal of Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75128768","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: 1
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