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Upper bound on the blowup rate of inhomogeneous NLS with Aharonov-Bohm magnetic potential
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-03-27 DOI: 10.1016/j.jmaa.2025.129529
Yuan Li
{"title":"Upper bound on the blowup rate of inhomogeneous NLS with Aharonov-Bohm magnetic potential","authors":"Yuan Li","doi":"10.1016/j.jmaa.2025.129529","DOIUrl":"10.1016/j.jmaa.2025.129529","url":null,"abstract":"<div><div>In this paper, we consider the mass-supercritical inhomogeneous nonlinear Schrödinger equation with an Aharonov-Bohm magnetic potential in the two dimensional case and obtain an upper bound on the blowup rate in the non-radial case.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129529"},"PeriodicalIF":1.2,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143737769","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
Explicit bounds for Bell numbers and their ratios
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-03-27 DOI: 10.1016/j.jmaa.2025.129527
Jerzy Grunwald, Grzegorz Serafin
{"title":"Explicit bounds for Bell numbers and their ratios","authors":"Jerzy Grunwald,&nbsp;Grzegorz Serafin","doi":"10.1016/j.jmaa.2025.129527","DOIUrl":"10.1016/j.jmaa.2025.129527","url":null,"abstract":"<div><div>In this article, we provide a comprehensive analysis of the asymptotic behavior of Bell numbers, enhancing and unifying various results previously dispersed in the literature. We establish several explicit lower and upper bounds. The main results correspond to two asymptotic forms expressed by means of the Lambert <em>W</em> function. As an application, some straightforward elementary bounds are derived. Additionally, an absolute convergence rate of the ratio of consecutive Bell numbers is derived. One of the main challenges was to obtain satisfactory constants, as the Bell numbers grow rapidly, while the convergence rates are rather slow.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129527"},"PeriodicalIF":1.2,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143737770","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
On Zhang-Yang's open question about iterative roots of PM functions of height 1 (II): Decreasing case
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-03-26 DOI: 10.1016/j.jmaa.2025.129517
Siyi Zhao , Liu Liu , Weinian Zhang
{"title":"On Zhang-Yang's open question about iterative roots of PM functions of height 1 (II): Decreasing case","authors":"Siyi Zhao ,&nbsp;Liu Liu ,&nbsp;Weinian Zhang","doi":"10.1016/j.jmaa.2025.129517","DOIUrl":"10.1016/j.jmaa.2025.129517","url":null,"abstract":"<div><div>A Zhang-Yang's open question reads: Does a PM function <em>F</em> with height <span><math><mi>H</mi><mo>(</mo><mi>F</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></span> have an iterative root <em>f</em> of order <span><math><mi>n</mi><mo>≤</mo><mi>N</mi><mo>(</mo><mi>F</mi><mo>)</mo><mo>+</mo><mn>1</mn></math></span> if the ‘characteristic endpoints condition’ is not satisfied? This question was answered in the case that <em>F</em> is strictly increasing on its characteristic interval <span><math><mi>K</mi><mo>(</mo><mi>F</mi><mo>)</mo></math></span>. However, a more difficult case is that <em>F</em> is strictly decreasing on <span><math><mi>K</mi><mo>(</mo><mi>F</mi><mo>)</mo></math></span>. In this paper we discuss the decreasing case, giving existence of <em>f</em> of order <span><math><mi>n</mi><mo>&lt;</mo><mi>N</mi><mo>(</mo><mi>F</mi><mo>)</mo></math></span> with <span><math><mi>H</mi><mo>(</mo><mi>f</mi><mo>)</mo><mo>=</mo><mi>n</mi></math></span> and of order <span><math><mi>n</mi><mo>≤</mo><mi>N</mi><mo>(</mo><mi>F</mi><mo>)</mo><mo>+</mo><mn>1</mn></math></span> with <span><math><mi>H</mi><mo>(</mo><mi>f</mi><mo>)</mo><mo>=</mo><mi>n</mi><mo>−</mo><mn>1</mn></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129517"},"PeriodicalIF":1.2,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143739646","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
Asymptotic analysis of the nonsteady micropolar fluid flow through a system of thin pipes revisited: Boundary-layer-in-time effects
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-03-26 DOI: 10.1016/j.jmaa.2025.129519
Grigory Panasenko , Igor Pažanin , Borja Rukavina
{"title":"Asymptotic analysis of the nonsteady micropolar fluid flow through a system of thin pipes revisited: Boundary-layer-in-time effects","authors":"Grigory Panasenko ,&nbsp;Igor Pažanin ,&nbsp;Borja Rukavina","doi":"10.1016/j.jmaa.2025.129519","DOIUrl":"10.1016/j.jmaa.2025.129519","url":null,"abstract":"<div><div>In this paper, we revisit the problem of the time-dependent micropolar fluid flow in a thin pipe system considered in Pažanin et al. (2024) <span><span>[29]</span></span>. We remove the restriction that the inflow/outflow and the external source functions vanish for small values of time and extend the analysis to non-homogeneous initial conditions. This requires the construction of the boundary-layer-in-time and the boundary-layer-in-space-and-in-time correctors in the asymptotic expansion of the solution. Consequently, we propose a new asymptotic approximation of higher order of accuracy for a general case with strong coupling between velocity and microrotation. The error estimates are also proved justifying the use of the derived effective model and indicating its range of applicability.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129519"},"PeriodicalIF":1.2,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143739758","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
Unique solutions to power-transformed affine systems
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-03-25 DOI: 10.1016/j.jmaa.2025.129515
John Stachurski , Ole Wilms , Junnan Zhang
{"title":"Unique solutions to power-transformed affine systems","authors":"John Stachurski ,&nbsp;Ole Wilms ,&nbsp;Junnan Zhang","doi":"10.1016/j.jmaa.2025.129515","DOIUrl":"10.1016/j.jmaa.2025.129515","url":null,"abstract":"<div><div>Systems of the form <span><math><mi>x</mi><mo>=</mo><msup><mrow><mo>(</mo><mi>A</mi><msup><mrow><mi>x</mi></mrow><mrow><mi>s</mi></mrow></msup><mo>)</mo></mrow><mrow><mn>1</mn><mo>/</mo><mi>s</mi></mrow></msup><mo>+</mo><mi>b</mi></math></span> arise in a range of economic and financial applications, where <em>A</em> is a linear operator acting on a space of real-valued functions (or vectors) and <em>s</em> is a nonzero real value. In these applications, attention is focused on positive solutions. We provide a simple characterization of existence and uniqueness of positive solutions when <em>b</em> is positive and <em>A</em> is irreducible.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129515"},"PeriodicalIF":1.2,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143705439","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
Riesz transforms for bi-Schrödinger operators on weighted Lebesgue spaces
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-03-24 DOI: 10.1016/j.jmaa.2025.129516
Nguyen Ngoc Trong , Le Xuan Truong , Tan Duc Do
{"title":"Riesz transforms for bi-Schrödinger operators on weighted Lebesgue spaces","authors":"Nguyen Ngoc Trong ,&nbsp;Le Xuan Truong ,&nbsp;Tan Duc Do","doi":"10.1016/j.jmaa.2025.129516","DOIUrl":"10.1016/j.jmaa.2025.129516","url":null,"abstract":"<div><div>Let <span><math><mi>d</mi><mo>∈</mo><mo>{</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mo>…</mo><mo>}</mo></math></span> and a weight <span><math><mi>w</mi><mo>∈</mo><msubsup><mrow><mi>A</mi></mrow><mrow><mo>∞</mo></mrow><mrow><mi>ρ</mi></mrow></msubsup></math></span>. We consider the fourth-order Riesz transform <span><math><mi>T</mi><mo>=</mo><msup><mrow><mi>∇</mi></mrow><mrow><mn>4</mn></mrow></msup><mspace></mspace><msup><mrow><mi>L</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span> associated with the bi-Schrödinger operator <span><math><mi>L</mi><mo>=</mo><msup><mrow><mi>Δ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>V</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, where <span><math><mi>V</mi><mo>∈</mo><mi>R</mi><msub><mrow><mi>H</mi></mrow><mrow><mi>σ</mi></mrow></msub><mo>∩</mo><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> with <span><math><mi>σ</mi><mo>&gt;</mo><mfrac><mrow><mn>2</mn><mi>d</mi></mrow><mrow><mn>3</mn></mrow></mfrac></math></span> and <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> stands for a Gaussian class of potentials. We show that <em>T</em> is bounded on <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><mi>w</mi></mrow><mrow><mi>p</mi></mrow></msubsup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></math></span> for all <em>p</em> in a suitable range depending on <em>σ</em>. If more conditions are imposed on either <em>σ</em> or <em>V</em>, the range for <em>p</em> can be extended to <span><math><mo>(</mo><mn>1</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"548 2","pages":"Article 129516"},"PeriodicalIF":1.2,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143697914","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
Identities for the product of two Dirichlet series satisfying Hecke's functional equation
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-03-24 DOI: 10.1016/j.jmaa.2025.129514
Bruce C. Berndt, Likun Xie
{"title":"Identities for the product of two Dirichlet series satisfying Hecke's functional equation","authors":"Bruce C. Berndt,&nbsp;Likun Xie","doi":"10.1016/j.jmaa.2025.129514","DOIUrl":"10.1016/j.jmaa.2025.129514","url":null,"abstract":"<div><div>We derive a general formula for the product of two Dirichlet series that satisfy Hecke's functional equation. Several examples are provided to demonstrate the applicability of the formula. In addition, we discuss prior work on similar products and clarify certain issues arising in the existing literature.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129514"},"PeriodicalIF":1.2,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143739757","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
On asymptotics of oscillatory solutions to nth-order delay differential equations
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-03-24 DOI: 10.1016/j.jmaa.2025.129507
Elena Braverman , Alexander Domoshnitsky , John Ioannis Stavroulakis
{"title":"On asymptotics of oscillatory solutions to nth-order delay differential equations","authors":"Elena Braverman ,&nbsp;Alexander Domoshnitsky ,&nbsp;John Ioannis Stavroulakis","doi":"10.1016/j.jmaa.2025.129507","DOIUrl":"10.1016/j.jmaa.2025.129507","url":null,"abstract":"<div><div>We study bounded and decaying to zero solutions of the delay differential equation<span><span><span><math><msup><mrow><mi>x</mi></mrow><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></msup><mo>(</mo><mi>t</mi><mo>)</mo><mo>+</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>m</mi></mrow></munderover><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo><mi>x</mi><mo>(</mo><mi>t</mi><mo>−</mo><msub><mrow><mi>τ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo><mo>)</mo><mo>=</mo><mn>0</mn><mspace></mspace><mtext>for</mtext><mspace></mspace><mi>t</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>,</mo><mspace></mspace><mi>t</mi><mo>≥</mo><mn>0</mn><mo>,</mo><mi>x</mi><mo>(</mo><mi>ξ</mi><mo>)</mo><mo>=</mo><mi>φ</mi><mo>(</mo><mi>ξ</mi><mo>)</mo><mspace></mspace><mtext>for </mtext><mspace></mspace><mi>ξ</mi><mo>&lt;</mo><mn>0</mn><mo>.</mo></math></span></span></span> Kondrat'ev and Kiguradze introduced and defined principles of asymptotic behavior for its solution in the sense of the trichotomy: oscillatory, non-oscillatory with absolute values monotonically decaying to zero or monotonically increasing to ∞. Expanding upon such studies, we estimate the oscillation amplitudes of solutions. Decay to zero is established through fast oscillation: once distances between zeros are small enough, the Grönwall inequality growth estimate implies the amplitudes decrease to zero as <span><math><mi>t</mi><mo>→</mo><mo>∞</mo></math></span>. Exact growth estimates and calculation of these distances between zeros are proposed through evaluation for the spectral radii of some compact operators associated with the Green's function for an <em>n</em>-point problem.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129507"},"PeriodicalIF":1.2,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143739612","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
Composition of locally solid convergences
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-03-24 DOI: 10.1016/j.jmaa.2025.129511
Eugene Bilokopytov
{"title":"Composition of locally solid convergences","authors":"Eugene Bilokopytov","doi":"10.1016/j.jmaa.2025.129511","DOIUrl":"10.1016/j.jmaa.2025.129511","url":null,"abstract":"<div><div>We carry on a more detailed investigation of the composition of locally solid convergences as introduced in <span><span>[6]</span></span>, as well as the corresponding notion of idempotency considered in <span><span>[4]</span></span>. In particular, we study the interactions between these two concepts and various operations with convergences. We prove associativity of the composition and show that the adherence of an ideal with respect to an idempotent convergence is equal to its closure. Some results from <span><span>[12]</span></span> about unbounded modification of locally solid topologies are generalized to the level of locally solid idempotent convergences. A simple application of the composition allows us to answer a question from <span><span>[6]</span></span> about minimal Hausdorff locally solid convergences. We also show that the weakest Hausdorff locally solid convergence exists on an Archimedean vector lattice if and only if it is atomic.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129511"},"PeriodicalIF":1.2,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143704573","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
Global dynamics of Liénard systems with arbitrary degrees
IF 1.2 3区 数学
Journal of Mathematical Analysis and Applications Pub Date : 2025-03-24 DOI: 10.1016/j.jmaa.2025.129503
Hebai Chen, Zhijie Li, Yu Xiao, Xin Yang
{"title":"Global dynamics of Liénard systems with arbitrary degrees","authors":"Hebai Chen,&nbsp;Zhijie Li,&nbsp;Yu Xiao,&nbsp;Xin Yang","doi":"10.1016/j.jmaa.2025.129503","DOIUrl":"10.1016/j.jmaa.2025.129503","url":null,"abstract":"<div><div>The aim of this paper is to study global dynamics of Liénard systems with arbitrary degrees <span><math><mover><mrow><mi>x</mi></mrow><mrow><mo>˙</mo></mrow></mover><mo>=</mo><mi>y</mi></math></span>, <span><math><mover><mrow><mi>y</mi></mrow><mrow><mo>˙</mo></mrow></mover><mo>=</mo><msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>x</mi><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msub><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn><mi>m</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mo>(</mo><msub><mrow><mi>a</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn>4</mn></mrow></msub><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo><mi>y</mi></math></span>. The complex and rich dynamics are presented, in particular, including double limit cycle bifurcation, Hopf bifurcation, homoclinic bifurcation and heteroclinic bifurcation. We illustrate theoretical results by numerical simulations.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129503"},"PeriodicalIF":1.2,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143705437","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
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