Analysis and Mathematical Physics最新文献_第6页

Multiple normalized solutions to critical Choquard equation involving fractional p-Laplacian in ({mathbb {R}}^{N})

IF 1.4 3区数学

Analysis and Mathematical Physics Pub Date : 2025-01-25 DOI: 10.1007/s13324-025-01011-7

Xin Zhang, Thin Van Nguyen, Sihua Liang

{"title":"Multiple normalized solutions to critical Choquard equation involving fractional p-Laplacian in ({mathbb {R}}^{N})","authors":"Xin Zhang, Thin Van Nguyen, Sihua Liang","doi":"10.1007/s13324-025-01011-7","DOIUrl":"10.1007/s13324-025-01011-7","url":null,"abstract":"<div><p>The paper mainly investigates the existence of multiple normalized solutions for critical Choquard equation with involving fractional <i>p</i>-Laplacian in <span>({mathbb {R}}^{N})</span>: </p><div><div><span>$$begin{aligned} left{ ! begin{array}{lll} (-Delta )_{p}^{s}u !+!Z(kappa x)|u|^{p-2}u!=!lambda |u|^{p-2}u!+! Big [dfrac{1}{|x|^{N-alpha }}*|u|^{q}!Big ]|u|^{q-2}u!+!sigma |u|^{p_{s}^{*}-2}u & text{ in } {mathbb {R}}^{N}!, displaystyle int _{{mathbb {R}}^{N}}|u|^{p}dx=a^{p}, end{array} right. end{aligned}$$</span></div></div><p>where <span>(kappa > 0)</span> is a small parameter, <span>(lambda in {mathbb {R}})</span> is a Lagrange multiplier, <span>(Z:{mathbb {R}}^{N}rightarrow [0,infty ))</span> is a continuous function. Under the right conditions, together with the minimization techniques, truncated method, variational methods and the Lusternik–Schnirelmann category, we obtain the existence of multiple normalized solutions, which can be viewed as a partial extension of the previous results concerning the existence of normalized solutions to this problem in the case of <span>(s = 1)</span>, <span>(p = 2)</span> and subcritical case.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109582","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

Endpoint regularity of general Fourier integral operators

IF 1.4 3区数学

Analysis and Mathematical Physics Pub Date : 2025-01-24 DOI: 10.1007/s13324-025-01013-5

Wenjuan Li, Xiangrong Zhu

引用次数: 0

Fractional integral operators in variable exponent Stummel spaces 变指数Stummel空间中的分数阶积分算子

IF 1.4 3区数学

Analysis and Mathematical Physics Pub Date : 2025-01-15 DOI: 10.1007/s13324-024-01006-w

Alexandre Almeida, Humberto Rafeiro

引用次数: 0

New limits of the Lie product formula type in Banach algebras Banach代数中李积公式类型的新极限

IF 1.4 3区数学

Analysis and Mathematical Physics Pub Date : 2025-01-14 DOI: 10.1007/s13324-024-01002-0

Dumitru Popa

{"title":"New limits of the Lie product formula type in Banach algebras","authors":"Dumitru Popa","doi":"10.1007/s13324-024-01002-0","DOIUrl":"10.1007/s13324-024-01002-0","url":null,"abstract":"<div><p>We find new limits of the Lie product formula type in Banach algebras with unit. Some sample results: Let <i>X</i>, <i>Y</i>, <i>Z</i> be Banach algebras with unit, <span>( left( x_{n},y_{n}right) _{nin mathbb {N}}subset Xtimes Y)</span> convergent sequences with <span>(lim nolimits _{nrightarrow infty }x_{n}=x)</span>, <span>( lim nolimits _{nrightarrow infty }y_{n}=y)</span> and <span>(T:Xtimes Yrightarrow Z)</span> a continuous bilinear operator with <span>(Tleft( textbf{1},textbf{1}right) = textbf{1})</span>. Then for all sequences of natural numbers <span>(left( a_{n}right) _{nin mathbb {N}})</span> with <span>(lim nolimits _{nrightarrow infty }a_{n}=infty )</span> we have </p><div><div><span>$$begin{aligned} lim limits _{nrightarrow infty }left[ Tleft( prod limits _{k=1}^{n}e^{ frac{x_{k}}{a_{n}left( k+nright) left( k+2nright) }},prod limits _{k=1}^{n}e^{frac{y_{k}}{a_{n}left( k+2nright) left( k+3nright) } }right) right] ^{a_{n}}=e^{left( ln frac{4}{3}right) Tleft( x,textbf{ 1}right) +left( ln 2right) Tleft( textbf{1},yright) }; end{aligned}$$</span></div></div><div><div><span>$$begin{aligned} lim limits _{nrightarrow infty }left[ Tleft( prod limits _{k=1}^{n}cos frac{x_{k}}{a_{n}sqrt{nleft( n+kright) }},prod limits _{k=1}^{n}cos frac{ky_{k}}{na_{n}sqrt{n^{2}+k^{2}}}right) right] ^{na_{n}^{2}} end{aligned}$$</span></div></div><div><div><span>$$begin{aligned} =e^{-frac{left( ln 2right) Tleft( x^{2},textbf{1}right) +left( 1- frac{pi }{4}right) Tleft( textbf{1},y^{2}right) }{2}}. end{aligned}$$</span></div></div></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-01002-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142976575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Eigenvalues of the magnetic Dirichlet Laplacian with constant magnetic field on disks in the strong field limit 强磁场极限下圆盘上磁场恒定的狄利克雷拉普拉斯算子的特征值

IF 1.4 3区数学

Analysis and Mathematical Physics Pub Date : 2025-01-10 DOI: 10.1007/s13324-024-01008-8

Matthias Baur, Timo Weidl

引用次数: 0

Unimodularity and invariant volume forms for Hamiltonian dynamics on coisotropic Poisson homogeneous spaces 同向同性泊松齐次空间上哈密顿动力学的单模性和不变体积形式

IF 1.4 3区数学

Analysis and Mathematical Physics Pub Date : 2025-01-08 DOI: 10.1007/s13324-024-01003-z

I. Gutierrez-Sagredo, D. Iglesias-Ponte, J. C. Marrero, E. Padrón

引用次数: 0

Boundedness of solutions of Chern-Simons-Higgs systems involving the (Delta _{lambda })-Laplacian 涉及(Delta _{lambda }) -拉普拉斯算子的chen - simons - higgs系统解的有界性

IF 1.4 3区数学

Analysis and Mathematical Physics Pub Date : 2025-01-07 DOI: 10.1007/s13324-024-01004-y

Nguyen Van Biet, Anh Tuan Duong, Yen Thi Ngoc Ha

{"title":"Boundedness of solutions of Chern-Simons-Higgs systems involving the (Delta _{lambda })-Laplacian","authors":"Nguyen Van Biet, Anh Tuan Duong, Yen Thi Ngoc Ha","doi":"10.1007/s13324-024-01004-y","DOIUrl":"10.1007/s13324-024-01004-y","url":null,"abstract":"<div><p>The purpose of this paper is to study the boundedness of solutions of the Chern-Simons-Higgs equation </p><div><div><span>$$begin{aligned} partial _tw-Delta _{lambda } w = left| w right| ^2 left( beta ^2-left| w right| ^2right) w-frac{1}{2}left( beta ^2-left| w right| ^2 right) ^2w text{ in } mathbb {R}times mathbb {R}^N end{aligned}$$</span></div></div><p>and system </p><div><div><span>$$begin{aligned} {left{ begin{array}{ll} partial _t u -Delta _lambda u = u^2left( 1-u^2-gamma v^2right) u-frac{1}{2}left( 1-u^2-gamma v^2 right) ^2u & text { in } mathbb {R}times mathbb {R}^N, partial _t v -Delta _lambda v = v^2left( 1-v^2-gamma u^2right) v-frac{1}{2}left( 1-v^2-gamma u^2 right) ^2v & text { in }mathbb {R}times mathbb {R}^N, end{array}right. } end{aligned}$$</span></div></div><p>where <span>(gamma >0)</span>, <span>(beta )</span> is a bounded continuous function and <span>(Delta _{lambda })</span> is the strongly degenerate operator defined by </p><div><div><span>$$begin{aligned} Delta _{lambda }:=sum _{i=1}^N partial _{x_i}left( lambda _i^2partial _{x_i} right) . end{aligned}$$</span></div></div><p>Under some general hypotheses of <span>(lambda _i)</span>, we shall establish some boundedness properties of solutions of the equation and system above. Our result can be seen as an extension of that in [<i>Li, Yayun; Lei, Yutian, Boundedness for solutions of equations of the Chern-Simons-Higgs type. Appl. Math. Lett.88(2019), 8-12.</i>]. In addition, we provide a simple proof of the boundedness of solutions.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142939138","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

Noether symmetries of test charges in the magnetic monopole field 磁单极子场中测试电荷的诺特对称性

IF 1.4 3区数学

Analysis and Mathematical Physics Pub Date : 2025-01-06 DOI: 10.1007/s13324-024-01005-x

César S. López-Monsalvo, Alberto Rubio-Ponce

引用次数: 0

On the Laplace operator with a weak magnetic field in exterior domains 外域弱磁场下的拉普拉斯算子

IF 1.4 3区数学

Analysis and Mathematical Physics Pub Date : 2024-12-27 DOI: 10.1007/s13324-024-01001-1

Ayman Kachmar, Vladimir Lotoreichik, Mikael Sundqvist

引用次数: 0

Riesz capacity: monotonicity, continuity, diameter and volume Riesz容量：单调性、连续性、直径和体积