Journal of Mathematical Analysis and Applications最新文献

{"title":"Some properties of new sequence spaces based on Riordan numbers","authors":"Naim L. Braha ,&nbsp;Toufik Mansour","doi":"10.1016/j.jmaa.2024.128902","DOIUrl":"10.1016/j.jmaa.2024.128902","url":null,"abstract":"<div><div>In this paper, we define a new class of sequence spaces via Riordan numbers and prove their topological properties, and inclusion relations, obtain Schauder basis, and describe <span><math><mi>α</mi><mo>,</mo><mi>β</mi></math></span> and <em>γ</em> duals of them. We have given conditions under which there is matrix transformation between those new sequence spaces and the well-known classical sequence spaces. In the last part, we are given some results related to some special operator classes, such as approximable operators, nuclear operators, and ideal operators.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142318877","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 multi-bump solutions for the Schrödinger equation with slow decaying competing potentials","authors":"Boling Tang ,&nbsp;Hui Guo ,&nbsp;Tao Wang","doi":"10.1016/j.jmaa.2024.128904","DOIUrl":"10.1016/j.jmaa.2024.128904","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We are concerned with the existence of multi-bump solutions to the following nonlinear Schrödinger equation with competing potentials &lt;em&gt;V&lt;/em&gt; and &lt;em&gt;Q&lt;/em&gt;,&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&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;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Q&lt;/mi&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;msup&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mtext&gt;in&lt;/mtext&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&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;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/span&gt;, &lt;em&gt;V&lt;/em&gt; and &lt;em&gt;Q&lt;/em&gt; are radial functions having the following slow algebraic decay with &lt;span&gt;&lt;math&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;,&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mi&gt;V&lt;/mi&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;msub&gt;&lt;mrow&gt;&lt;mi&gt;V&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;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;κ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;Q&lt;/mi&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;msub&gt;&lt;mrow&gt;&lt;mi&gt;Q&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;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mtext&gt; as &lt;/mtext&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;mtext&gt;,&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;V&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;msub&gt;&lt;mrow&gt;&lt;mi&gt;Q&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;κ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;. By introducing a weighted norm and some delicate analysis, we construct infinitely many new positive multi-bump solutions for &lt;span&gt;&lt;math&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; or &lt;span&gt;&lt;math&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;. The maximum points of these bump solutions lie on the top and bottom circles of a cylinder near the infinity. This result complements and extends the existence results of multi-bump solutions in &lt;span&gt;&lt;span&gt;[2]&lt;/span&gt;&lt;/span&gt;, &lt;s","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142318879","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":"Sobolev projection on quantum torus, its complete boundedness and applications","authors":"Fedor Sukochev ,&nbsp;Kanat Tulenov ,&nbsp;Dmitriy Zanin","doi":"10.1016/j.jmaa.2024.128906","DOIUrl":"10.1016/j.jmaa.2024.128906","url":null,"abstract":"<div><div>In this paper, we establish the complete boundedness of Sobolev projection from <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mi>θ</mi></mrow><mrow><mi>d</mi></mrow></msubsup><mo>)</mo></math></span> into <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn><mo>,</mo><mo>∞</mo></mrow></msub><mo>(</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mi>θ</mi></mrow><mrow><mi>d</mi></mrow></msubsup><mo>)</mo></math></span>. In the special case <span><math><mi>θ</mi><mo>=</mo><mn>0</mn></math></span>, our results strengthen the classical results due to Berkson, Bourgain, Pelczynski and Wojciechowski.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425179","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":"On Haagerup noncommutative quasi Hp(A) spaces","authors":"Turdebek N. Bekjan","doi":"10.1016/j.jmaa.2024.128905","DOIUrl":"10.1016/j.jmaa.2024.128905","url":null,"abstract":"<div><div>Let <span><math><mi>M</mi></math></span> be a <em>σ</em>-finite von Neumann algebra, equipped with a normal faithful state <em>φ</em>, and let <span><math><mi>A</mi></math></span> be a maximal subdiagonal subalgebra of <span><math><mi>M</mi></math></span>. We have proved that for <span><math><mn>0</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mn>1</mn></math></span>, <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>A</mi><mo>)</mo></math></span> is independent of <em>φ</em>. Furthermore, in the case that <span><math><mi>A</mi></math></span> is a type 1 subdiagonal subalgebra, we have obtained an interpolation theorem for <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>A</mi><mo>)</mo></math></span> in the case where <span><math><mn>0</mn><mo>&lt;</mo><mi>θ</mi><mo>&lt;</mo><mn>1</mn></math></span>, <span><math><mn>0</mn><mo>&lt;</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>≤</mo><mo>∞</mo></math></span> and <span><math><mi>p</mi><mo>=</mo><mfrac><mrow><mn>1</mn><mo>−</mo><mi>θ</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></mfrac><mo>+</mo><mfrac><mrow><mi>θ</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfrac><mo>≥</mo><mn>1</mn></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142324154","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":"Approximation orders of real numbers in beta-dynamical systems","authors":"Xiaoqiong Wang ,&nbsp;Rao Li ,&nbsp;Fan Lü","doi":"10.1016/j.jmaa.2024.128895","DOIUrl":"10.1016/j.jmaa.2024.128895","url":null,"abstract":"<div><div>For any real numbers <span><math><mi>x</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> and <span><math><mi>β</mi><mo>&gt;</mo><mn>1</mn></math></span>, denote by <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>,</mo><mi>β</mi><mo>)</mo></math></span> the partial sum of the first <em>n</em> terms in the <em>β</em>-expansion of <em>x</em>. It is known that for any <span><math><mi>β</mi><mo>&gt;</mo><mn>1</mn></math></span> and almost all <span><math><mi>x</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>, or for any <span><math><mi>x</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> and almost all <span><math><mi>β</mi><mo>&gt;</mo><mn>1</mn></math></span>, the approximation order of <em>x</em> by <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>,</mo><mi>β</mi><mo>)</mo></math></span> is <span><math><msup><mrow><mi>β</mi></mrow><mrow><mo>−</mo><mi>n</mi></mrow></msup></math></span>. Let <span><math><mi>φ</mi><mo>:</mo><mi>N</mi><mo>→</mo><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span> be a positive function. In this paper, we study the Hausdorff dimensions of the following two sets<span><span><span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>β</mi></mrow></msub><mo>(</mo><mi>φ</mi><mo>)</mo><mo>=</mo><mrow><mo>{</mo><mi>x</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo><mo>:</mo><munder><mrow><mrow><mi>lim</mi></mrow><mspace></mspace><mrow><mi>sup</mi></mrow></mrow><mrow><mi>n</mi><mo>→</mo><mo>∞</mo></mrow></munder><mspace></mspace><mfrac><mrow><msub><mrow><mi>log</mi></mrow><mrow><mi>β</mi></mrow></msub><mo>⁡</mo><mo>(</mo><mi>x</mi><mo>−</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>,</mo><mi>β</mi><mo>)</mo><mo>)</mo></mrow><mrow><mi>φ</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mfrac><mo>=</mo><mo>−</mo><mn>1</mn><mo>}</mo></mrow><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>x</mi></mrow></msub><mo>(</mo><mi>φ</mi><mo>)</mo><mo>=</mo><mrow><mo>{</mo><mi>β</mi><mo>&gt;</mo><mn>1</mn><mo>:</mo><munder><mrow><mrow><mi>lim</mi></mrow><mspace></mspace><mrow><mi>sup</mi></mrow></mrow><mrow><mi>n</mi><mo>→</mo><mo>∞</mo></mrow></munder><mspace></mspace><mfrac><mrow><msub><mrow><mi>log</mi></mrow><mrow><mi>β</mi></mrow></msub><mo>⁡</mo><mo>(</mo><mi>x</mi><mo>−</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>,</mo><mi>β</mi><mo>)</mo><mo>)</mo></mrow><mrow><mi>φ</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mfrac><mo>=</mo><mo>−</mo><mn>1</mn><mo>}</mo></mrow><mo>,</mo></math></span></span></span> and complement the dimension theoretic results of these sets in <span><span>[3]</span></span>, <span><span>[6]</span></span> and <span><span>[18]</span></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142324040","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":"Best Ulam constants for damped linear oscillators with variable coefficients","authors":"Douglas R. Anderson ,&nbsp;Masakazu Onitsuka ,&nbsp;Donal O'Regan","doi":"10.1016/j.jmaa.2024.128908","DOIUrl":"10.1016/j.jmaa.2024.128908","url":null,"abstract":"<div><div>An associated Riccati equation is used to study the Ulam stability of non-autonomous linear differential equations that model the damped linear oscillator. In particular, the best (minimal) Ulam constants for these equations are derived. These robust results apply to equations with solutions that blow up in finite time, as well as to equations with solutions that exist globally on <span><math><mo>(</mo><mo>−</mo><mo>∞</mo><mo>,</mo><mo>∞</mo><mo>)</mo></math></span>. Illustrative, non-trivial examples are presented, highlighting the main results.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425181","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":"Wave-front tracking for a quasi-linear scalar conservation law with hysteresis","authors":"Fabio Bagagiolo,&nbsp;Stefan Moreti","doi":"10.1016/j.jmaa.2024.128900","DOIUrl":"10.1016/j.jmaa.2024.128900","url":null,"abstract":"<div><div>In this article we deal with the Cauchy problem for the quasi-linear scalar conservation law<span><span><span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mi>F</mi><msub><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>x</mi></mrow></msub><mo>=</mo><mn>0</mn><mo>,</mo></math></span></span></span> where <span><math><mi>F</mi></math></span> is a specific hysteresis operator, namely the Play operator. Hysteresis models a rate-independent memory relationship between the input <em>u</em> and its output. Its presence in the partial differential equation gives a particular non-local feature to the latter allowing us to capture phenomena that may arise in some application fields. Riemann problems and the interactions between shock lines are studied and via the so-called Wave-Front Tracking method a solution to the Cauchy problem with bounded variation initial data is constructed. The solution found satisfies an entropy-like condition, making it the unique solution in the class of entropy admissible ones.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425183","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}

{"title":"An invariant for affine maximal type equations","authors":"Zhao Lian","doi":"10.1016/j.jmaa.2024.128898","DOIUrl":"10.1016/j.jmaa.2024.128898","url":null,"abstract":"<div><div>Let <span><math><mi>y</mi><mo>:</mo><mi>M</mi><mo>→</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span> be a locally strongly convex hypersurface immersion of a smooth, connected manifold into the real affine space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span>, given as the graph of a smooth, strictly convex function <span><math><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><mi>f</mi><mo>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span> defined on a domain <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. Considering the <em>α</em>-relative normalization of the graph of the convex function <em>f</em>, we will prove a Bernstein theorem for a class of nonlinear, fourth order partial differential equations of affine maximal type. As applications, we define an invariant of the equations and prove a rigidity result of the complete <span><math><msup><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>-invariant Kähler metric on complex torus <span><math><msup><mrow><mo>(</mo><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup></math></span> with vanishing scalar curvature for <span><math><mi>n</mi><mo>≤</mo><mn>5</mn></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142318878","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":"A note on kernel functions of Dirichlet spaces","authors":"Sahil Gehlawat ,&nbsp;Aakanksha Jain ,&nbsp;Amar Deep Sarkar","doi":"10.1016/j.jmaa.2024.128897","DOIUrl":"10.1016/j.jmaa.2024.128897","url":null,"abstract":"<div><div>For a planar domain Ω, we consider the Dirichlet spaces with respect to a base point <span><math><mi>ζ</mi><mo>∈</mo><mi>Ω</mi></math></span> and the corresponding kernel functions. It is not known how these kernel functions behave as we vary the base point. In this note, we prove that these kernel functions vary smoothly. As an application of the smoothness result, we prove a Ramadanov-type theorem for these kernel functions on <span><math><mi>Ω</mi><mo>×</mo><mi>Ω</mi></math></span>. This extends the previously known convergence results of these kernel functions. In fact, we have made these observations in a more general setting, that is, for weighted kernel functions and their higher-order counterparts.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142318876","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":"Ap weights and an application to Hankel operators on Fock spaces with variable exponents on Cn","authors":"Agbor Dieudonne Agbor,&nbsp;Forwa Kingsley Njem","doi":"10.1016/j.jmaa.2024.128899","DOIUrl":"10.1016/j.jmaa.2024.128899","url":null,"abstract":"<div><div>We characterize <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> weights for <span><math><mi>p</mi><mo>&gt;</mo><mn>1</mn></math></span> and via extrapolation we characterize boundedness and compactness of Hankel operators between Fock spaces of variable exponent and the Lebesgue spaces of variable exponents. We also give some characterizations of the symbol class which is some <em>BMO</em>-type spaces with variable exponent on the complex plane <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425198","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}