Advanced Nonlinear Studies最新文献_第3页

On constant higher order mean curvature hypersurfaces in H n × R ${mathbb{H}}^{n}{times}mathbb{R}$ 论 H n × R ${mathbb{H}}^{n}{times}mathbb{R}$ 中的恒定高阶均值曲率超曲面

IF 1.8 2区数学

Advanced Nonlinear Studies Pub Date : 2024-03-15 DOI: 10.1515/ans-2023-0115

Barbara Nelli, Giuseppe Pipoli, Giovanni Russo

{"title":"On constant higher order mean curvature hypersurfaces in H n × R ${mathbb{H}}^{n}{times}mathbb{R}$","authors":"Barbara Nelli, Giuseppe Pipoli, Giovanni Russo","doi":"10.1515/ans-2023-0115","DOIUrl":"https://doi.org/10.1515/ans-2023-0115","url":null,"abstract":"We classify hypersurfaces with rotational symmetry and positive constant r-th mean curvature in <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mrow> <m:mi mathvariant=\"double-struck\">H</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msup> <m:mo>×</m:mo> <m:mi mathvariant=\"double-struck\">R</m:mi> </m:math> ${mathbb{H}}^{n}{times}mathbb{R}$ . Specific constant higher order mean curvature hypersurfaces invariant under hyperbolic translation are also treated. Some of these invariant hypersurfaces are employed as barriers to prove a Ros–Rosenberg type theorem in <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mrow> <m:mi mathvariant=\"double-struck\">H</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msup> <m:mo>×</m:mo> <m:mi mathvariant=\"double-struck\">R</m:mi> </m:math> ${mathbb{H}}^{n}{times}mathbb{R}$ : we show that compact connected hypersurfaces of constant r-th mean curvature embedded in <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mrow> <m:mi mathvariant=\"double-struck\">H</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msup> <m:mo>×</m:mo> <m:mrow> <m:mo stretchy=\"false\">[</m:mo> <m:mrow> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:mi>∞</m:mi> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:math> ${mathbb{H}}^{n}{times}left[0,infty right)$ with boundary in the slice <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mrow> <m:mi mathvariant=\"double-struck\">H</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msup> <m:mo>×</m:mo> <m:mrow> <m:mo stretchy=\"false\">{</m:mo> <m:mrow> <m:mn>0</m:mn> </m:mrow> <m:mo stretchy=\"false\">}</m:mo> </m:mrow> </m:math> ${mathbb{H}}^{n}{times}left{0right}$ are topological disks under suitable assumptions.","PeriodicalId":7191,"journal":{"name":"Advanced Nonlinear Studies","volume":"51 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140153185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 existence and multiplicity of L 2-normalized solutions to nonlinear Schrödinger equations with variable coefficients 具有可变系数的非线性薛定谔方程的 L 2 归一化解的存在性和多重性

IF 1.8 2区数学

Advanced Nonlinear Studies Pub Date : 2024-03-14 DOI: 10.1515/ans-2022-0056

Norihisa Ikoma, Mizuki Yamanobe

{"title":"The existence and multiplicity of L 2-normalized solutions to nonlinear Schrödinger equations with variable coefficients","authors":"Norihisa Ikoma, Mizuki Yamanobe","doi":"10.1515/ans-2022-0056","DOIUrl":"https://doi.org/10.1515/ans-2022-0056","url":null,"abstract":"The existence of L 2–normalized solutions is studied for the equation <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mo>−</m:mo> <m:mi mathvariant=\"normal\">Δ</m:mi> <m:mi>u</m:mi> <m:mo>+</m:mo> <m:mi>μ</m:mi> <m:mi>u</m:mi> <m:mo>=</m:mo> <m:mi>f</m:mi> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo>,</m:mo> <m:mi>u</m:mi> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> <m:mtext> </m:mtext> <m:mtext> </m:mtext> <m:mtext>in</m:mtext> <m:mspace width=\"0.3333em\" /> <m:msup> <m:mrow> <m:mi mathvariant=\"bold\">R</m:mi> </m:mrow> <m:mrow> <m:mi>N</m:mi> </m:mrow> </m:msup> <m:mo>,</m:mo> <m:mspace width=\"1em\" /> <m:msub> <m:mrow> <m:mo>∫</m:mo> </m:mrow> <m:mrow> <m:msup> <m:mrow> <m:mi mathvariant=\"bold\">R</m:mi> </m:mrow> <m:mrow> <m:mi>N</m:mi> </m:mrow> </m:msup> </m:mrow> </m:msub> <m:msup> <m:mrow> <m:mi>u</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msup> <m:mspace width=\"0.17em\" /> <m:mi mathvariant=\"normal\">d</m:mi> <m:mi>x</m:mi> <m:mo>=</m:mo> <m:mi>m</m:mi> <m:mo>.</m:mo> </m:math> $-{Delta}u+mu u=fleft(x,uright)quad quad text{in} {mathbf{R}}^{N},quad {int }_{{mathbf{R}}^{N}}{u}^{2} mathrm{d}x=m.$ Here m > 0 and f(x, s) are given, f(x, s) has the L 2-subcritical growth and (μ, u) ∈ R × H 1(R N ) are unknown. In this paper, we employ the argument in Hirata and Tanaka (“Nonlinear scalar field equations with L 2 constraint: mountain pass and symmetric mountain pass approaches,” Adv. Nonlinear Stud., vol. 19, no. 2, pp. 263–290, 2019) and find critical points of the Lagrangian function. To obtain critical points of the Lagrangian function, we use the Palais–Smale–Cerami condition instead of Condition (PSP) in Hirata and Tanaka (“Nonlinear scalar field equations with L 2 constraint: mountain pass and symmetric mountain pass approaches,” Adv. Nonlinear Stud., vol. 19, no. 2, pp. 263–290, 2019). We also prove the multiplicity result under the radial symmetry.","PeriodicalId":7191,"journal":{"name":"Advanced Nonlinear Studies","volume":"305 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140153186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 free or prescribed mass solutions for fractional Hartree equations and Pohozaev identities 分数哈特里方程和波霍扎耶夫等式的无限多自由或规定质量解

IF 1.8 2区数学

Advanced Nonlinear Studies Pub Date : 2024-03-14 DOI: 10.1515/ans-2023-0110

Silvia Cingolani, Marco Gallo, Kazunaga Tanaka

引用次数: 0

Sharp affine weighted L 2 Sobolev inequalities on the upper half space 上半空间上的尖锐仿射加权 L 2 索波列夫不等式

IF 1.8 2区数学

Advanced Nonlinear Studies Pub Date : 2024-03-14 DOI: 10.1515/ans-2023-0117

Jingbo Dou, Yunyun Hu, Caihui Yue

引用次数: 0

An upper bound for the least energy of a sign-changing solution to a zero mass problem 零质量问题符号变化解的最小能量上限

IF 1.8 2区数学

Advanced Nonlinear Studies Pub Date : 2024-03-14 DOI: 10.1515/ans-2022-0065

Mónica Clapp, Liliane Maia, Benedetta Pellacci

{"title":"An upper bound for the least energy of a sign-changing solution to a zero mass problem","authors":"Mónica Clapp, Liliane Maia, Benedetta Pellacci","doi":"10.1515/ans-2022-0065","DOIUrl":"https://doi.org/10.1515/ans-2022-0065","url":null,"abstract":"We give an upper bound for the least possible energy of a sign-changing solution to the nonlinear scalar field equation <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <m:mo>−</m:mo> <m:mi mathvariant=\"normal\">Δ</m:mi> <m:mi>u</m:mi> <m:mo>=</m:mo> <m:mi>f</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mi>u</m:mi> <m:mo>)</m:mo> </m:mrow> <m:mo>,</m:mo> <m:mspace width=\"0.17em\" /> <m:mi>u</m:mi> <m:mo>∈</m:mo> <m:msup> <m:mi>D</m:mi> <m:mn>1,2</m:mn> </m:msup> <m:mrow> <m:mo>(</m:mo> <m:msup> <m:mi mathvariant=\"normal\">R</m:mi> <m:mi>N</m:mi> </m:msup> <m:mo>)</m:mo> </m:mrow> <m:mo>,</m:mo> </m:math> $-{Delta}u=fleft(uright), uin {D}^{1,2}left({mathrm{R}}^{N}right),$ where N ≥ 5 and the nonlinearity f is subcritical at infinity and supercritical near the origin. More precisely, we establish the existence of a nonradial sign-changing solution whose energy is smaller that 12c 0 if N = 5, 6 and smaller than 10c 0 if N ≥ 7, where c 0 is the ground state energy.","PeriodicalId":7191,"journal":{"name":"Advanced Nonlinear Studies","volume":"143 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140153187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 C 2,α,β estimate for complex Monge–Ampère type equations with conic sigularities 具有圆锥西格的复杂蒙日-安培方程的 C 2,α,β 估计值

IF 1.8 2区数学

Advanced Nonlinear Studies Pub Date : 2024-03-13 DOI: 10.1515/ans-2023-0113

Liding Huang, Gang Tian, Jiaxiang Wang

引用次数: 0

Geometry of branched minimal surfaces of finite index 有限指数分支极小曲面的几何学

IF 1.8 2区数学

Advanced Nonlinear Studies Pub Date : 2024-03-12 DOI: 10.1515/ans-2023-0118

William H. Meeks, Joaquín Pérez

{"title":"Geometry of branched minimal surfaces of finite index","authors":"William H. Meeks, Joaquín Pérez","doi":"10.1515/ans-2023-0118","DOIUrl":"https://doi.org/10.1515/ans-2023-0118","url":null,"abstract":"Given <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <m:mi>I</m:mi> <m:mo>,</m:mo> <m:mi>B</m:mi> <m:mo>∈</m:mo> <m:mi mathvariant=\"double-struck\">N</m:mi> <m:mo>∪</m:mo> <m:mrow> <m:mo stretchy=\"false\">{</m:mo> <m:mrow> <m:mn>0</m:mn> </m:mrow> <m:mo stretchy=\"false\">}</m:mo> </m:mrow> </m:math> <jats:tex-math> $I,Bin mathbb{N}cup left{0right}$ </jats:tex-math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_ans-2023-0118_ineq_001.png\" /> </jats:alternatives> </jats:inline-formula>, we investigate the existence and geometry of complete finitely branched minimal surfaces <jats:italic>M</jats:italic> in <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <m:msup> <m:mrow> <m:mi mathvariant=\"double-struck\">R</m:mi> </m:mrow> <m:mrow> <m:mn>3</m:mn> </m:mrow> </m:msup> </m:math> <jats:tex-math> ${mathbb{R}}^{3}$ </jats:tex-math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_ans-2023-0118_ineq_002.png\" /> </jats:alternatives> </jats:inline-formula> with Morse index at most <jats:italic>I</jats:italic> and total branching order at most <jats:italic>B</jats:italic>. Previous works of Fischer-Colbrie (“On complete minimal surfaces with finite Morse index in 3-manifolds,” <jats:italic>Invent. Math.</jats:italic>, vol. 82, pp. 121–132, 1985) and Ros (“One-sided complete stable minimal surfaces,” <jats:italic>J. Differ. Geom.</jats:italic>, vol. 74, pp. 69–92, 2006) explain that such surfaces are precisely the complete minimal surfaces in <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <m:msup> <m:mrow> <m:mi mathvariant=\"double-struck\">R</m:mi> </m:mrow> <m:mrow> <m:mn>3</m:mn> </m:mrow> </m:msup> </m:math> <jats:tex-math> ${mathbb{R}}^{3}$ </jats:tex-math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_ans-2023-0118_ineq_003.png\" /> </jats:alternatives> </jats:inline-formula> of finite total curvature and finite total branching order. Among other things, we derive scale-invariant weak chord-arc type results for such an <jats:italic>M</jats:italic> with estimates that are given in terms of <jats:italic>I</jats:italic> and <jats:italic>B</jats:italic>. In order to obtain some of our main results for these special surfaces, we obtain general intrinsic monotonicity of area formulas for <jats:italic>m</jats:italic>-dimensional submanifolds Σ of an <jats:italic>n</jats:italic>-dimensional Riemannian manifold <jats:italic>X</jats:italic>, where these area estimates depend on the geometry of <jats:italic>X</jats:italic> and upper bounds on the lengths of the mean curvature vectors of Σ. We also describe a family of complete, finitely branched minimal surfaces in <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" ","PeriodicalId":7191,"journal":{"name":"Advanced Nonlinear Studies","volume":"58 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140114990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Segregated solutions for nonlinear Schrödinger systems with a large number of components 具有大量分量的非线性薛定谔系统的分离解

IF 1.8 2区数学

Advanced Nonlinear Studies Pub Date : 2024-03-12 DOI: 10.1515/ans-2022-0076

Haixia Chen, Angela Pistoia

引用次数: 0

A semilinear Dirichlet problem involving the fractional Laplacian in R+ n 涉及 R+ n 中分数拉普拉斯的半线性迪里夏特问题

IF 1.8 2区数学

Advanced Nonlinear Studies Pub Date : 2024-03-12 DOI: 10.1515/ans-2023-0102

Yan Li

引用次数: 0

Liouville theorems of solutions to mixed order Hénon-Hardy type system with exponential nonlinearity 指数非线性混合阶 Hénon-Hardy 型系统解的 Liouville 定理