Journal of Mathematical Analysis and Applications最新文献

{"title":"Lp Liouville type theorems for harmonic functions on gradient Ricci solitons","authors":"Yong Luo","doi":"10.1016/j.jmaa.2025.129901","DOIUrl":"10.1016/j.jmaa.2025.129901","url":null,"abstract":"<div><div>In this paper we consider <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> Liouville type theorems for harmonic functions on gradient Ricci solitons. In particular, assume that <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>)</mo></math></span> is a gradient shrinking or steady Kähler-Ricci soliton, then we prove that any pluriharmonic function <em>u</em> on <em>M</em> with <span><math><mi>∇</mi><mi>u</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>M</mi><mo>)</mo></math></span> for some <span><math><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>≤</mo><mn>2</mn></math></span> is a constant function.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 2","pages":"Article 129901"},"PeriodicalIF":1.2,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144670519","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}

{"title":"Heisenberg-Pauli-Weyl uncertainty principles for the fractional Dunkl transform on the real line","authors":"Sunit Ghosh,&nbsp;Younis Ahmad Bhat,&nbsp;Jitendriya Swain","doi":"10.1016/j.jmaa.2025.129890","DOIUrl":"10.1016/j.jmaa.2025.129890","url":null,"abstract":"<div><div>The aim of the paper is two-fold. First, we provide an explicit form of the functions for which equality holds for the uncertainty inequalities studied in <span><span>[11]</span></span>. Second, we establish an <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-type Heisenberg-Pauli-Weyl uncertainty principle for the fractional Dunkl transform, with <span><math><mn>1</mn><mo>≤</mo><mi>p</mi><mo>≤</mo><mn>2</mn></math></span>. For the case <span><math><mi>p</mi><mo>=</mo><mn>2</mn></math></span>, we further derive a sharper uncertainty principle for the fractional Dunkl transform. Furthermore, we derive conditions leading to equality in both the uncertainty principles obtained.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 1","pages":"Article 129890"},"PeriodicalIF":1.2,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144672209","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}

{"title":"Semilinear elliptic equations with singular potentials and nonlinearities","authors":"Wanwan Wang ,&nbsp;Ying Wang ,&nbsp;Qingyong Liao","doi":"10.1016/j.jmaa.2025.129893","DOIUrl":"10.1016/j.jmaa.2025.129893","url":null,"abstract":"<div><div>This paper is concerned with semilinear elliptic equations <span><math><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mfrac><mrow><mi>μ</mi></mrow><mrow><msup><mrow><mi>ρ</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mi>u</mi><mo>=</mo><mfrac><mrow><mi>λ</mi></mrow><mrow><msup><mrow><mo>(</mo><mi>a</mi><mo>−</mo><mi>u</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></math></span> in a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> bounded convex domain Ω of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>, subject to the zero Dirichlet boundary conditions, where <span><math><mi>μ</mi><mo>∈</mo><mo>(</mo><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>,</mo><mn>0</mn><mo>)</mo></math></span> and <span><math><mi>ρ</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mrow><mi>dist</mi></mrow><mo>(</mo><mi>x</mi><mo>,</mo><mo>∂</mo><mi>Ω</mi><mo>)</mo></math></span>. We analyze the properties of minimal solutions when <span><math><mi>λ</mi><mo>&gt;</mo><mn>0</mn></math></span> and the function <span><math><mi>a</mi><mo>:</mo><mover><mrow><mi>Ω</mi></mrow><mrow><mo>¯</mo></mrow></mover><mo>→</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> satisfying <span><math><mi>a</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>≥</mo><mi>κ</mi><mi>ρ</mi><msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mrow><mi>γ</mi></mrow></msup></math></span> for some <span><math><mi>κ</mi><mo>&gt;</mo><mn>0</mn></math></span> and <span><math><mi>γ</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mfrac><mrow><mn>3</mn><mo>+</mo><msqrt><mrow><mn>1</mn><mo>+</mo><mn>4</mn><mi>μ</mi></mrow></msqrt></mrow><mrow><mn>4</mn></mrow></mfrac><mo>)</mo></math></span>. Moreover, the regularity and stability of the extremal solution are obtained.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 2","pages":"Article 129893"},"PeriodicalIF":1.2,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144654592","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}

{"title":"p-summable localization ⁎-algebras and Roe ⁎-algebras","authors":"Hang Wang ,&nbsp;Chaohua Zhang ,&nbsp;Dapeng Zhou","doi":"10.1016/j.jmaa.2025.129888","DOIUrl":"10.1016/j.jmaa.2025.129888","url":null,"abstract":"<div><div>Inspired by the notion of <em>p</em>-summable Fredholm modules, we introduce <em>p</em>-summable localization ⁎-algebras and <em>p</em>-summable Roe ⁎-algebras, and prove that they are dense ⁎-subalgebras of localization algebras and Roe algebras respectively.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 1","pages":"Article 129888"},"PeriodicalIF":1.2,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655538","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}

{"title":"Stability of weighted log canonical threshold of plurisubharmonic functions","authors":"Trinh Tung","doi":"10.1016/j.jmaa.2025.129887","DOIUrl":"10.1016/j.jmaa.2025.129887","url":null,"abstract":"<div><div>Let <em>φ</em> be a plurisubharmonic function on an open subset <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. We know that <em>φ</em> has a singularity at point <em>a</em> if <span><math><mi>φ</mi><mo>(</mo><mi>a</mi><mo>)</mo><mo>=</mo><mo>−</mo><mo>∞</mo></math></span>. Two of the most important measures of singularities are the Lelong number and the log canonical threshold. In this article, we study the stability of weighted log canonical thresholds <span><math><msub><mrow><mi>c</mi></mrow><mrow><mi>μ</mi></mrow></msub><mo>(</mo><mi>φ</mi><mo>)</mo></math></span> with measure <span><math><mi>μ</mi><mo>=</mo><msup><mrow><mo>(</mo><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>m</mi></mrow></msubsup><mo>|</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>k</mi></mrow></msub><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mi>t</mi></mrow></msup><mi>d</mi><msub><mrow><mi>V</mi></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msub></math></span> for any <span><math><mi>t</mi><mo>∈</mo><mi>R</mi></math></span>. The result obtained leads to a principle for comparing Nadel's multiplier ideal sheaves.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 2","pages":"Article 129887"},"PeriodicalIF":1.2,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144654591","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}

{"title":"Boundedness and reproducing kernels of multiplier operators in the Fourier-Laguerre setting","authors":"Raoudha Laffi","doi":"10.1016/j.jmaa.2025.129886","DOIUrl":"10.1016/j.jmaa.2025.129886","url":null,"abstract":"<div><div>This paper investigates the Laguerre multiplier operator <span><math><msubsup><mrow><mi>M</mi></mrow><mrow><mi>u</mi><mo>,</mo><mi>β</mi></mrow><mrow><mi>α</mi></mrow></msubsup></math></span> within the Fourier-Laguerre transform framework. We begin by deriving Calderón reproducing formulas, including an inversion formula and a method for approximating square-integrable functions. We then establish uncertainty principles for <span><math><msubsup><mrow><mi>M</mi></mrow><mrow><mi>u</mi><mo>,</mo><mi>β</mi></mrow><mrow><mi>α</mi></mrow></msubsup></math></span>, extending the Pauli-Weyl inequality and introducing a concentration-type inequality. These results demonstrate the enhanced capabilities of the multiplier operator compared to the classical Fourier transform, offering improved uncertainty bounds and advanced tools for harmonic analysis in the Fourier-Laguerre context.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 2","pages":"Article 129886"},"PeriodicalIF":1.2,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144633701","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}

{"title":"Linear preservers of parallel/TEA vectors in Lp(μ) spaces","authors":"Chi-Kwong Li ,&nbsp;Ming-Cheng Tsai ,&nbsp;Ya-Shu Wang ,&nbsp;Ngai-Ching Wong","doi":"10.1016/j.jmaa.2025.129889","DOIUrl":"10.1016/j.jmaa.2025.129889","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In normed vector spaces, two vectors &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; are &lt;em&gt;parallel&lt;/em&gt; (resp., &lt;em&gt;triangle equality attaining&lt;/em&gt; (TEA)) if there is a scalar &lt;em&gt;ξ&lt;/em&gt; with &lt;span&gt;&lt;math&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;ξ&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; (resp., &lt;span&gt;&lt;math&gt;&lt;mi&gt;ξ&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;) such that &lt;span&gt;&lt;math&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;ξ&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. This paper characterizes linear maps preserving these pairs in &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; spaces, where non-strict convexity enables rich geometric structures absent in &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; spaces, with &lt;span&gt;&lt;math&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∪&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; (for which all linear maps trivially preserve such pairs). We first resolve finite-dimensional cases: &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ℓ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;-norm TEA pair preservers are matrices with at most one nonzero entry per row. For &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ℓ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, TEA pair preservers are scalar multiples of isometries, except in &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;. These results extend to infinite dimensional spaces &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ℓ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Λ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Λ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ℓ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Λ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, where TEA pair preservers are generalized permutation operators (for &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ℓ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;) or scalar multiples of isometries (for &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ℓ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;). In all cases, parallel pair preservers are either TEA pair preservers or rank one maps. Crucially, we generalize to measure-theoretic settings. For &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, TEA pair preservers are automatically bounded and preserves disjointness; in many interesting cases, they are weighted compositions. Parallel pair preservers combine these with rank-one maps. For &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/m","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 2","pages":"Article 129889"},"PeriodicalIF":1.2,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144654593","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}

{"title":"Long-time asymptotics for a fourth-order dispersive nonlinear Schrödinger equation with nonzero boundary conditions","authors":"Wei-Qi Peng ,&nbsp;Yong Chen","doi":"10.1016/j.jmaa.2025.129879","DOIUrl":"10.1016/j.jmaa.2025.129879","url":null,"abstract":"<div><div>In this work, we consider the long-time asymptotics of the Cauchy problem for a fourth-order dispersive nonlinear Schrödinger equation with nonzero boundary conditions at infinity. Firstly, in order to construct the basic Riemann-Hilbert problem associated with nonzero boundary conditions, we analyze direct scattering problem. The nonlinear steepest descent method is employed to transform the matrix Riemann-Hilbert problem into a solvable model. Furthermore, the <em>g</em>-function mechanism is applied to effectively eliminate the exponential growth in the jump matrix. We obtain the long-time asymptotic behavior in the modulated elliptic wave region and the plane wave region for the fourth-order dispersive nonlinear Schrödinger equation. Finally, we also provide an analysis of the modulation instability of the initial plane wave.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 2","pages":"Article 129879"},"PeriodicalIF":1.2,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144654589","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}

{"title":"Positive periodic solutions for systems of linear functional differential inequalities","authors":"Robert Hakl ,&nbsp;José Oyarce","doi":"10.1016/j.jmaa.2025.129882","DOIUrl":"10.1016/j.jmaa.2025.129882","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Consider the system of functional differential inequalities&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;ℓ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mtext&gt;for a. e. &lt;/mtext&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;mi&gt;ℓ&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is a linear bounded operator, &lt;span&gt;&lt;math&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, and &lt;span&gt;&lt;math&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;diag&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;…&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. In the present paper, we establish conditions guaranteeing that there exists &lt;span&gt;&lt;math&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; such that every absolutely continuous &lt;em&gt;ω&lt;/em&gt;-periodic vector-valued function &lt;span&gt;&lt;math&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; satisfying the above-mentioned differential inequality belongs to a cone&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mtext&gt; for &lt;/mtext&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;…&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; We denote the set of periodic linear operators &lt;em&gt;ℓ&lt;/em&gt; with the above property by &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;U&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mr","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 2","pages":"Article 129882"},"PeriodicalIF":1.2,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144654590","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}

{"title":"Stochastic homogenization of dynamical discrete optimal transport","authors":"Peter Gladbach,&nbsp;Eva Kopfer","doi":"10.1016/j.jmaa.2025.129883","DOIUrl":"10.1016/j.jmaa.2025.129883","url":null,"abstract":"<div><div>The aim of this paper is to examine the large-scale behavior of dynamical optimal transport on stationary random graphs embedded in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. Our central theorem is a stochastic homogenization result that characterizes the effective behavior of the discrete problems in terms of a continuous optimal transport problem, where the homogenized energy density results from the geometry of the discrete graph.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"553 2","pages":"Article 129883"},"PeriodicalIF":1.2,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144614841","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}