Annali di Matematica Pura ed Applicata最新文献_第6页

Polar actions on homogeneous 3-spaces 齐次三维空间上的极性作用

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2025-12-24 DOI: 10.1007/s10231-025-01627-3

Miguel Domínguez-Vázquez, Tarcios A. Ferreira, Tomás Otero

引用次数: 0

Large solutions to semilinear equations for subordinate Laplacians in (C^{1,1}) bounded open sets (C^{1,1})有界开集中下拉普拉斯半线性方程的大解

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2025-12-19 DOI: 10.1007/s10231-025-01637-1

Indranil Chowdhury, Zoran Vondraček, Vanja Wagner

引用次数: 0

Asymptotic behavior of positive solutions to a slightly subcritical Choquard equation 一类微次临界Choquard方程正解的渐近性质

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2025-12-15 DOI: 10.1007/s10231-025-01635-3

Jinkai Gao

{"title":"Asymptotic behavior of positive solutions to a slightly subcritical Choquard equation","authors":"Jinkai Gao","doi":"10.1007/s10231-025-01635-3","DOIUrl":"10.1007/s10231-025-01635-3","url":null,"abstract":"<div><p>In this paper, we consider the following slightly subcritical Choquard equation </p><div><div><span>$$begin{aligned} {left{ begin{array}{ll} -Delta u=left( int _{Omega }frac{u^{2^*_{alpha }-varepsilon }(y)}{|x-y|^alpha }dyright) u^{2^*_{alpha }-1-varepsilon },quad u>0, & text{ in } Omega , quad u=0, & text{ on } partial Omega , end{array}right. } end{aligned}$$</span></div></div><p>where <span>(Nge 3)</span>, <span>(Omega )</span> is a smooth bounded domain in <span>(mathbb {R}^{N})</span>, <span>(alpha in (0,N))</span>, <span>(2^*_{alpha }:=frac{2N-alpha }{N-2})</span> is the upper critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality, and <span>(varepsilon >0)</span> is a small parameter. For the energy-minimizing solutions, we characterize their asymptotic profiles, derive their blow-up rates, and prove that their blow-up points are critical points of the Robin function. Moreover, through orthogonal decomposition, we obtain refined estimates for both the blow-up rate and concentration speed. For the least energy solutions, which form a particular family of the energy-minimizing solutions, we establish a precise energy expansion and further prove that the blow-up point globally minimizes the Robin function. The main results of this paper demonstrate that the asymptotic behavior of solutions to the above equation depends on both the spatial dimension <i>N</i> and the geometry of domain <span>(Omega )</span>. In contrast to the local case studied in the literature, the nonlocal Choquard term brings several difficulties, and new estimates are required.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 3","pages":"1151 - 1208"},"PeriodicalIF":0.9,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148268740","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

Sharp existence to a nonlinear Schrödinger equation in bounded domains via double constraints and bifurcation theory 利用双约束和分岔理论研究有界域上非线性Schrödinger方程的尖锐存在性

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2025-12-15 DOI: 10.1007/s10231-025-01636-2

Jiaqing Hu, Anmin Mao

{"title":"Sharp existence to a nonlinear Schrödinger equation in bounded domains via double constraints and bifurcation theory","authors":"Jiaqing Hu, Anmin Mao","doi":"10.1007/s10231-025-01636-2","DOIUrl":"10.1007/s10231-025-01636-2","url":null,"abstract":"<div><p>We study the following nonlinear Schrödinger equation in bounded domains </p><div><div><span>$$begin{aligned} left{ begin{array}{ll} - left( {a + bint _Omega {|nabla u{|^2}dx} } right) Delta u = lambda u + mu (x){|u|^{p - 2}u} & quad {textrm{in}}; Omega , int _{Omega } {|u|^2dx} = c,; u = 0 & quad {textrm{on}}; partial Omega . end{array} right. end{aligned}$$</span></div></div><p>In the case of <span>(b=0)</span>, <span>(a=1)</span> and <span>(mu (x)=1)</span>, existence of the solutions with prescribed mass was obtained (see Noris et al. in Anal PDE 7:1807–1838, 2014, Pierotti and Verzini in Calc Var 56:133, 2017). For the general case, in particular sign-changing <span>(mu (x))</span>, similar existence results to the above problem is still unknown. Here we focus on these unknown case and get sharp existence results via new ideas. When <span>(2 + frac{8}{N}< p < 2^*)</span>, we find constants <span>(c^*> c_* >0)</span>, and prove the existence of at least two normalized solutions for <span>(0<c<c_*)</span> and at least one normalized solution for <span>(c_*< c <c^*)</span>. In particular, when <span>(mu (x))</span> is a positive constant, the existence of any <span>(k in mathbb {N}^+)</span> normalized solutions is proved. When <span>(2 < p le 2 + frac{8}{N})</span>, we search for a global minimizer of energy functional as normalized solution to the equation, where three cases of <span>(mu (x) ge 0)</span>, <span>(mu (x) le 0)</span> and <span>(mu (x))</span> changing sign are analyzed. Finally, if <span>( mu )</span> is regarded as an unknown real number, one normalized solution is obtained by the analysis of variational problem with double constraints. Tables 1 and 2 will clearly illustrate our main results and the relationship between our work and some related works in the literature.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 3","pages":"1209 - 1241"},"PeriodicalIF":0.9,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148268639","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

Defect of compactness for the Moser-Trudinger inequality Moser-Trudinger不等式的紧致缺陷

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2025-12-08 DOI: 10.1007/s10231-025-01644-2

Giuseppe Devillanova, Cyril Tintarev

引用次数: 0

Infinitely many solutions to a conformally invariant elliptic equation with Choquard-type nonlinearity 一类具有choquard型非线性的共形不变椭圆方程的无穷多解

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2025-12-05 DOI: 10.1007/s10231-025-01646-0

Mona Almutairi, Mathew Gluck

引用次数: 0

A nonvariational Neumann problem for the Helmholtz equation 亥姆霍兹方程的非变分诺伊曼问题

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2025-11-27 DOI: 10.1007/s10231-025-01614-8

Massimo Lanza de Cristoforis

引用次数: 0

The nonlinear porous medium equation for the f-Laplacian: Hamilton-Souplet-Zhang type gradient estimates and implications f- laplace的非线性多孔介质方程：Hamilton-Souplet-Zhang型梯度估计及其意义

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2025-11-24 DOI: 10.1007/s10231-025-01639-z

Ali Taheri, Vahideh Vahidifar

引用次数: 0

Invariants for sum-rank metric codes 和秩度量码的不变量

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2025-11-23 DOI: 10.1007/s10231-025-01640-6

Paolo Santonastaso, Ferdinando Zullo

引用次数: 0

An abstract result for non-differentiable functionals and its applications to partial differential equations with singular nonlinearities 不可微泛函的一个抽象结果及其在奇异非线性偏微分方程中的应用

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2025-11-21 DOI: 10.1007/s10231-025-01641-5

Ricardo Lima Alves

引用次数: 0