Calculus of Variations and Partial Differential Equations最新文献_第8页

Multiplicity results for constant Q-curvature conformal metrics 恒Q曲率共形度量的多重性结果

IF 2.1 2区数学

Calculus of Variations and Partial Differential Equations Pub Date : 2024-06-24 DOI: 10.1007/s00526-024-02762-0

Salomón Alarcón, Jimmy Petean, Carolina Rey

{"title":"Multiplicity results for constant Q-curvature conformal metrics","authors":"Salomón Alarcón, Jimmy Petean, Carolina Rey","doi":"10.1007/s00526-024-02762-0","DOIUrl":"https://doi.org/10.1007/s00526-024-02762-0","url":null,"abstract":"In this paper we provide a positive lower bound for the number of metrics of constant Q-curvature which are conformal to a Riemannian product of the form ((Mtimes X, g+delta h)), where (delta >0) is a small positive constant, (M, g) is a closed (compact without boundary) n-dimensional Riemannian manifold and (X, h) a closed m-dimensional (positive) Einstein manifold. We assume that (mge 3) and (nge 2) or, if (m=2), that (nge 7). More specifically, we study the constant Q-curvature equation on the Riemannian product ((Mtimes X, g+delta h)), which becomes, by restricting the equation to functions which depend only on the M-variable, a subcritical equation on (M, g) driven by a fourth order operator, known as the Paneitz operator. Then we prove that, for (delta >0) small enough, the equation has at least (textrm{Cat}(M)) positive solutions, where (textrm{Cat}(M)) is the Lusternik-Schnirelmann category of M. This implies that there are at least (textrm{Cat}(M)) metrics of constant Q-curvature in the conformal class of the Riemannian product ((Mtimes X, g+delta h)).","PeriodicalId":9478,"journal":{"name":"Calculus of Variations and Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141515270","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

Existence of singular isoperimetric regions in 8-dimensional manifolds 8 维流形中奇异等周区域的存在性

IF 2.1 2区数学

Calculus of Variations and Partial Differential Equations Pub Date : 2024-06-20 DOI: 10.1007/s00526-024-02748-y

Gongping Niu

引用次数: 0

On the critical exponent $$p_c$$ of the 3D quasilinear wave equation $$-big (1+(partial _tphi )^pbig )partial _t^2phi +Delta phi =0$$ with short pulse initial data: II—shock formation 关于具有短脉冲初始数据的三维准线性波方程 $$-big (1+(partial _tphi )^pbig )partial _t^2phi +Delta phi =0$$ 的临界指数 $$p_c$$：II-shock formation

IF 2.1 2区数学

Calculus of Variations and Partial Differential Equations Pub Date : 2024-06-18 DOI: 10.1007/s00526-024-02753-1

Lu Yu, Yin Huicheng

{"title":"On the critical exponent $$p_c$$ of the 3D quasilinear wave equation $$-big (1+(partial _tphi )^pbig )partial _t^2phi +Delta phi =0$$ with short pulse initial data: II—shock formation","authors":"Lu Yu, Yin Huicheng","doi":"10.1007/s00526-024-02753-1","DOIUrl":"https://doi.org/10.1007/s00526-024-02753-1","url":null,"abstract":"In the previous paper (Ding et al. in J Differ Equ 385:183–253, 2024), for the 3D quasilinear wave equation (-big (1+(partial _tphi )^pbig )partial _t^2phi +Delta phi =0) with short pulse initial data ((phi ,partial _tphi )(1,x)=big (delta ^{2-varepsilon _{0}}phi _0 (frac{r-1}{delta },omega ),delta ^{1-varepsilon _{0}}phi _1(frac{r-1}{delta },omega )big )), where (pin mathbb {N}), (0<varepsilon _{0}<1), under the outgoing constraint condition ((partial _t+partial _r)^kphi (1,x)=O(delta ^{2-varepsilon _{0}-kmax {0,1-(1-varepsilon _{0})p}})) for (k=1,2), the authors establish the global existence of smooth large solution (phi ) when (p>p_c) with (p_c=frac{1}{1-varepsilon _{0}}). In the present paper, under the same outgoing constraint condition, when (1le ple p_c), we will show that the smooth solution (phi ) may blow up and further the outgoing shock is formed in finite time.","PeriodicalId":9478,"journal":{"name":"Calculus of Variations and Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551999","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

Normalized solutions for a fractional Schrödinger–Poisson system with critical growth 具有临界增长的分数薛定谔-泊松系统的归一化解法

IF 2.1 2区数学

Calculus of Variations and Partial Differential Equations Pub Date : 2024-06-14 DOI: 10.1007/s00526-024-02749-x

Xiaoming He, Yuxi Meng, Marco Squassina

{"title":"Normalized solutions for a fractional Schrödinger–Poisson system with critical growth","authors":"Xiaoming He, Yuxi Meng, Marco Squassina","doi":"10.1007/s00526-024-02749-x","DOIUrl":"https://doi.org/10.1007/s00526-024-02749-x","url":null,"abstract":"In this paper, we study the fractional critical Schrödinger–Poisson system $$begin{aligned}{left{ begin{array}{ll} (-Delta )^su +lambda phi u= alpha u+mu |u|^{q-2}u+|u|^{2^*_s-2}u,&{}~~ hbox {in}~{mathbb {R}}^3, (-Delta )^tphi =u^2,&{}~~ hbox {in}~{mathbb {R}}^3,end{array}right. } end{aligned}$$having prescribed mass $$begin{aligned} int _{{mathbb {R}}^3} |u|^2dx=a^2,end{aligned}$$where ( s, t in (0, 1)) satisfy (2,s+2t> 3, qin (2,2^*_s), a>0) and (lambda ,mu >0) parameters and (alpha in {mathbb {R}}) is an undetermined parameter. For this problem, under the (L^2)-subcritical perturbation (mu |u|^{q-2}u, qin (2,2+frac{4,s}{3})), we derive the existence of multiple normalized solutions by means of the truncation technique, concentration-compactness principle and the genus theory. In the (L^2)-supercritical perturbation (mu |u|^{q-2}u,qin (2+frac{4,s}{3}, 2^*_s)), we prove two different results of normalized solutions when parameters (lambda ,mu ) satisfy different assumptions, by applying the constrained variational methods and the mountain pass theorem. Our results extend and improve some previous ones of Zhang et al. (Adv Nonlinear Stud 16:15–30, 2016); and of Teng (J Differ Equ 261:3061–3106, 2016), since we are concerned with normalized solutions.","PeriodicalId":9478,"journal":{"name":"Calculus of Variations and Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141515271","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

Rigidity of Schouten tensor under conformal deformation 保角变形下舒顿张量的刚性

IF 2.1 2区数学

Calculus of Variations and Partial Differential Equations Pub Date : 2024-06-14 DOI: 10.1007/s00526-024-02751-3

Mijia Lai, Guoqiang Wu

引用次数: 0

Counterexamples to the comparison principle in the special Lagrangian potential equation 特殊拉格朗日势能方程中比较原理的反例

IF 2.1 2区数学

Calculus of Variations and Partial Differential Equations Pub Date : 2024-06-05 DOI: 10.1007/s00526-024-02747-z

Karl K. Brustad

引用次数: 0

Regularized mean curvature flow for invariant hypersurfaces in a Hilbert space and its application to gauge theory 希尔伯特空间中不变超曲面的正则化平均曲率流及其在量规理论中的应用

IF 2.1 2区数学

Calculus of Variations and Partial Differential Equations Pub Date : 2024-06-05 DOI: 10.1007/s00526-024-02745-1

Naoyuki Koike

引用次数: 0

The Einstein-scalar field Lichnerowicz equations on graphs 图上的爱因斯坦-标量场李奇诺维茨方程

IF 2.1 2区数学

Calculus of Variations and Partial Differential Equations Pub Date : 2024-06-05 DOI: 10.1007/s00526-024-02737-1

Leilei Cui, Yong Liu, Chunhua Wang, Jun Wang, Wen Yang

引用次数: 0

Normalized solutions to Schrödinger equations in the strongly sublinear regime 强亚线性状态下薛定谔方程的归一化解

IF 2.1 2区数学

Calculus of Variations and Partial Differential Equations Pub Date : 2024-05-30 DOI: 10.1007/s00526-024-02729-1

Jarosław Mederski, Jacopo Schino

引用次数: 0

Torus-like solutions for the Landau-de Gennes model. Part III: torus vs split minimizers Landau-de Gennes 模型的环状解。第三部分：环状解与分裂最小解

IF 2.1 2区数学

Calculus of Variations and Partial Differential Equations Pub Date : 2024-05-27 DOI: 10.1007/s00526-024-02743-3

Federico Luigi Dipasquale, Vincent Millot, Adriano Pisante

引用次数: 0