Journal of Mathematical Analysis and Applications最新文献

{"title":"Normalized solutions of a (2,p)-Laplacian equation","authors":"Xiaoli Zhu,&nbsp;Yunli Zhao,&nbsp;Zhanping Liang","doi":"10.1016/j.jmaa.2025.129462","DOIUrl":"10.1016/j.jmaa.2025.129462","url":null,"abstract":"<div><div>In this paper, we are concerned with normalized solutions of a <span><math><mo>(</mo><mn>2</mn><mo>,</mo><mi>p</mi><mo>)</mo></math></span>-Laplacian equation with an <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> constraint in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>, where <span><math><mn>2</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mn>3</mn></math></span>. Different from literature previous, we focus on the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> not <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> constraint for <span><math><mi>p</mi><mo>&gt;</mo><mn>2</mn></math></span>. Moreover, an interesting finding is that the non-homogeneity driven by the operators Δ and <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> has an important impact on <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> constraint <span><math><mo>(</mo><mn>2</mn><mo>,</mo><mi>p</mi><mo>)</mo></math></span>-Laplacian equations, as reflected in the definition of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> critical exponent, and the existence of normalized solutions in both <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> subcritical and supercritical cases. All these new phenomena, which are different from those exhibited by a single <em>p</em>-Laplacian equation, reveal the essential characteristics of <span><math><mo>(</mo><mn>2</mn><mo>,</mo><mi>p</mi><mo>)</mo></math></span>-Laplacian equations.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129462"},"PeriodicalIF":1.2,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143636614","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":"Asymptotic expansions for the generalised trigonometric integral and its zeros","authors":"Gergő Nemes","doi":"10.1016/j.jmaa.2025.129463","DOIUrl":"10.1016/j.jmaa.2025.129463","url":null,"abstract":"<div><div>In this paper, we investigate the asymptotic properties of the generalised trigonometric integral <span><math><mi>ti</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>z</mi><mo>,</mo><mi>α</mi><mo>)</mo></math></span> and its associated modulus and phase functions for large complex values of <em>z</em>. We derive asymptotic expansions for these functions, accompanied by explicit and computable error bounds. For real values of <em>a</em>, the function <span><math><mi>ti</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>z</mi><mo>,</mo><mi>α</mi><mo>)</mo></math></span> possesses infinitely many positive real zeros. Assuming <span><math><mi>a</mi><mo>&lt;</mo><mn>1</mn></math></span>, we establish asymptotic expansions for the large zeros, accompanied by precise error estimates. The error bounds for the asymptotics of the phase function and its zeros will be derived by studying the analytic properties of both the phase function and its inverse. Additionally, we demonstrate that for real variables, the derived asymptotic expansions are enveloping, meaning that successive partial sums provide upper and lower bounds for the corresponding functions.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129463"},"PeriodicalIF":1.2,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143600801","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":"Semiclassical limit of a non-polynomial q-Askey scheme","authors":"Jonatan Lenells ,&nbsp;Julien Roussillon","doi":"10.1016/j.jmaa.2025.129474","DOIUrl":"10.1016/j.jmaa.2025.129474","url":null,"abstract":"<div><div>We prove a semiclassical asymptotic formula for the two elements <span><math><mi>M</mi></math></span> and <span><math><mi>Q</mi></math></span> lying at the bottom of the recently constructed non-polynomial hyperbolic <em>q</em>-Askey scheme. We also prove that the corresponding exponent is a generating function of the canonical transformation between pairs of Darboux coordinates on the monodromy manifold of the Painlevé I and <span><math><msub><mrow><mtext>III</mtext></mrow><mrow><mn>3</mn></mrow></msub></math></span> equations, respectively. Such pairs of coordinates characterize the asymptotics of the tau function of the corresponding Painlevé equation. We conjecture that the other members of the non-polynomial hyperbolic <em>q</em>-Askey scheme yield generating functions associated to the other Painlevé equations in the semiclassical limit.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129474"},"PeriodicalIF":1.2,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143600800","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":"Dynamics and optimal control of an SIVR immuno-epidemiological model with standard incidence","authors":"Xi-Chao Duan ,&nbsp;Chenyu Zhu ,&nbsp;Xue-Zhi Li ,&nbsp;Eric Numfor ,&nbsp;Maia Martcheva","doi":"10.1016/j.jmaa.2025.129449","DOIUrl":"10.1016/j.jmaa.2025.129449","url":null,"abstract":"<div><div>Based on the immuno-epidemiological model concept, we propose a susceptible–infected–vaccinated–recovered epidemic model with between-host transmission and within-host infection, where disease transmission between hosts is described by a standard incidence rate and the within-host infection process is governed by a bilinear incidence rate. The basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>ψ</mi><mo>)</mo></math></span> in the between-host model strongly depends on the within-host infection process. If <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>ψ</mi><mo>)</mo><mo>&lt;</mo><mn>1</mn></math></span>, the disease-free steady state <span><math><msup><mrow><mi>E</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span> of the between-host epidemic model is locally stable, and if <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>ψ</mi><mo>)</mo><mo>&gt;</mo><mn>1</mn></math></span>, the endemic steady state <span><math><msup><mrow><mi>E</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> of the between-host epidemic model is locally stable. If <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>0</mn><mo>)</mo><mo>&lt;</mo><mn>1</mn></math></span>, the disease-free steady state <span><math><msup><mrow><mi>E</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span> of the between-host epidemic model is globally stable. Furthermore, to better understand the roles of within-host treatment and between-host control in disease transmission, we formulated and studied an optimal control problem for the immuno-epidemiological model involving treatment and vaccination. Numerical simulations were conducted to demonstrate the effectiveness of the control strategies in various infection processes. The results showed that the duration of within-host treatment must be longer than the duration of vaccination to better control the spread of the disease.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129449"},"PeriodicalIF":1.2,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143636627","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":"Convergence at infinity for solutions of nonhomogeneous degenerate and singular elliptic equations in exterior domains","authors":"Leonardo P. Bonorino ,&nbsp;Lucas P. Dutra ,&nbsp;Filipe J. dos Santos","doi":"10.1016/j.jmaa.2025.129476","DOIUrl":"10.1016/j.jmaa.2025.129476","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In this work, we investigate the existence of the limit at infinity of weak solutions of the nonhomogeneous equation &lt;span&gt;&lt;math&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;div&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; in the exterior domain &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;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;﹨&lt;/mo&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;span&gt;&lt;math&gt;&lt;mi&gt;K&lt;/mi&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;/math&gt;&lt;/span&gt; is a compact set. Indeed, for any &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;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&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; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, we prove that the solutions converge at infinity if &lt;em&gt;A&lt;/em&gt; satisfies some growth conditions and &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&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;/msup&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; has some decay property. Moreover, for &lt;span&gt;&lt;math&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; we can show that the solutions converge at some rate and, for &lt;span&gt;&lt;math&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, the convergence holds even for some unbounded &lt;em&gt;f&lt;/em&gt;. In addition, for &lt;span&gt;&lt;math&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, we show that for any continuous function &lt;em&gt;ϕ&lt;/em&gt; defined on ∂&lt;em&gt;K&lt;/em&gt;, the problem&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;div&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mtext&gt; in &lt;/mtext&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;mi&gt;K&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;ϕ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mtext&gt; on &lt;/mtext&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; has a bounded weak solution in &lt;span&gt;&lt;math&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mover&gt;&lt;mrow&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;mi&gt;K&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;‾&lt;/mo&gt;&lt;/mover&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∩&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&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;mi&gt;K&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, provided &lt;em&gt;A&lt;/em&gt; and &lt;em&gt;f&lt;/em&gt; are suitable. Furthermore, if &lt;span&gt;&lt;math&gt;&lt;mi&gt;ϕ&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129476"},"PeriodicalIF":1.2,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143684950","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":"Free boundary problem governed by a non-linear diffusion-convection equation with Neumann condition","authors":"Adriana C. Briozzo","doi":"10.1016/j.jmaa.2025.129461","DOIUrl":"10.1016/j.jmaa.2025.129461","url":null,"abstract":"<div><div>We consider a one-dimensional free boundary problem governed by a nonlinear diffusion - convection equation with a Neumann condition at fixed face <span><math><mi>x</mi><mo>=</mo><mn>0</mn></math></span>, which is variable in time and a like Stefan convective condition on the free boundary. Through successive transformations, an integral representation of the problem is obtained that involves a system of coupled nonlinear integral equations. Existence of the solution is obtained for all times by using fixed point theorems.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129461"},"PeriodicalIF":1.2,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143621371","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":"The finite spectrum problems for Dirac operators","authors":"Fangyuan Zhang,&nbsp;Kun Li,&nbsp;Jinming Cai","doi":"10.1016/j.jmaa.2025.129444","DOIUrl":"10.1016/j.jmaa.2025.129444","url":null,"abstract":"<div><div>In the present paper, the finite spectrum problem of Dirac operators is studied. For each nonnegative integer <em>m</em>, we construct a class of regular Dirac operator which has at most <span><math><mi>n</mi><mo>=</mo><mn>2</mn><mi>m</mi><mo>+</mo><mn>1</mn></math></span> eigenvalues. The method presented is based on choosing the coefficients of the Dirac equation such that they are alternatively zero on consecutive subintervals and iterative construction of the characteristic function.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129444"},"PeriodicalIF":1.2,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143636615","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":"The algebra D(W) via strong Darboux transformations","authors":"Ignacio Bono Parisi,&nbsp;Ines Pacharoni","doi":"10.1016/j.jmaa.2025.129443","DOIUrl":"10.1016/j.jmaa.2025.129443","url":null,"abstract":"<div><div>The Matrix Bochner Problem aims to classify weight matrices <em>W</em> such that the algebra <span><math><mi>D</mi><mo>(</mo><mi>W</mi><mo>)</mo></math></span>, of all differential operators that have a sequence of matrix-valued orthogonal polynomials for <em>W</em> as eigenfunctions, contains a second-order differential operator. In <span><span>[5]</span></span> it is proven that, under certain assumptions, the solutions to the Matrix Bochner Problem can be obtained through a noncommutative bispectral Darboux transformation of some classical scalar weights. The main aim of this paper is to introduce the concept of strong Darboux transformation among weight matrices and explore the relationship between the algebras <span><math><mi>D</mi><mo>(</mo><mi>W</mi><mo>)</mo></math></span> and <span><math><mi>D</mi><mo>(</mo><mover><mrow><mi>W</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>)</mo></math></span> when <span><math><mover><mrow><mi>W</mi></mrow><mrow><mo>˜</mo></mrow></mover></math></span> is a strong Darboux transformation of <em>W</em>. Starting from a direct sum of classical scalar weights <span><math><mover><mrow><mi>W</mi></mrow><mrow><mo>˜</mo></mrow></mover></math></span>, and leveraging our complete knowledge of the algebra of <span><math><mi>D</mi><mo>(</mo><mover><mrow><mi>W</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>)</mo></math></span>, we can easily determine the algebra <span><math><mi>D</mi><mo>(</mo><mi>W</mi><mo>)</mo></math></span> of a weight <em>W</em> that is a strong Darboux transformation of <span><math><mover><mrow><mi>W</mi></mrow><mrow><mo>˜</mo></mrow></mover></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129443"},"PeriodicalIF":1.2,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143621370","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":"Analytical properties of derivative polynomials","authors":"Guo-Niu Han ,&nbsp;Hailing Li ,&nbsp;Shi-Mei Ma ,&nbsp;Jean Yeh ,&nbsp;Yeong-Nan Yeh","doi":"10.1016/j.jmaa.2025.129442","DOIUrl":"10.1016/j.jmaa.2025.129442","url":null,"abstract":"<div><div>We study analytical properties of derivative polynomials for tangent and secant, including recurrence relations, explicit formulas and expansion formulas. Firstly, we discuss the connections between central binomial coefficients and trigonometric functions. Secondly, we explore the similarity of derivative polynomials and Chebyshev polynomials. The idea is to choose the derivative polynomials as basis sets of a polynomial space. From this viewpoint, we give an expansion of the derivative polynomials for tangent in terms of the derivative polynomials for secant as well as a result in the reverse direction. Moreover, we get the Frobenius-type formulas for exterior peak and left peak polynomials. Finally, we discuss the connections between derivative polynomials and Eulerian polynomials.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129442"},"PeriodicalIF":1.2,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143679333","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":"Properties for transposition solutions to operator-valued BSEEs, and applications to robust second order necessary conditions for controlled SEEs","authors":"Guangdong Jing","doi":"10.1016/j.jmaa.2025.129445","DOIUrl":"10.1016/j.jmaa.2025.129445","url":null,"abstract":"<div><div>This article is concerned with the second order necessary conditions for the stochastic optimal control problem of stochastic evolution equation with model uncertainty when the traditional Pontryagin-type maximum principle holds trivially and does not provide any information depicting the optimal control. The diffusion terms of the state equations are allowed to be control dependent with convex control constraints. Transposition method is adopted to deal with the adjoint operator-valued backward stochastic evolution equations, especially the correction terms. Besides, weak convergence arguments are used to obtain the optimal uncertainty reference measure, in which the regularities of the state processes, variational processes, and adjoint processes in the transposition sense are characterized. Malliavin calculus is applied to pave the way for differentiation theorem of Lebesgue type to deduce the pointwise robust optimality conditions.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129445"},"PeriodicalIF":1.2,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143600802","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}