Journal of Mathematical Analysis and Applications最新文献

{"title":"Increasing sequences in ordered Banach spaces – New theorems and open problems","authors":"Jochen Glück","doi":"10.1016/j.jmaa.2025.129694","DOIUrl":"10.1016/j.jmaa.2025.129694","url":null,"abstract":"<div><div>An ordered Banach space <em>X</em> is said to have the Levi property or to be regular if every increasing order bounded net (equivalently, sequence) is norm convergent. We prove four theorems related to this classical concept:</div><div>(i) The Levi property follows from the – formally weaker – assumption that every increasing net that has a minimal upper bound is norm convergent. This motivates a discussion about in which sense the Levi property resembles the notion of order continuous norm from Banach lattice theory.</div><div>(ii) If <em>X</em> is separable and has normal cone, then the assumption that every increasing order bounded sequence has a supremum implies the Levi property. This generalizes a classical result about Banach lattices, but requires new ideas since one cannot work with disjoint sequences in the proof.</div><div>(iii) A version of Dini's theorem for ordered Banach spaces that is more general than what is typically stated in the literature. We use this to derive a sufficient condition for the space of all compact operators between two Banach lattices to have the Levi property.</div><div>(iv) Dini's theorem never holds on reflexive ordered Banach spaces with non-normal cone – i.e., on such a space one can always find an increasing sequence that converges weakly but not in norm.</div><div>We illustrate our results by various examples and counterexamples and pose three open problems.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129694"},"PeriodicalIF":1.2,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144170511","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":"Li-Yau estimates and Harnack inequalities for nonlinear slow diffusion equations on a smooth metric measure space","authors":"Ali Taheri,&nbsp;Vahideh Vahidifar","doi":"10.1016/j.jmaa.2025.129691","DOIUrl":"10.1016/j.jmaa.2025.129691","url":null,"abstract":"<div><div>We present new gradient estimates and Harnack inequalities for positive solutions to nonlinear slow diffusion equations. The framework is that of a smooth metric measure space <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>,</mo><mi>d</mi><mi>μ</mi><mo>)</mo></math></span> with invariant weighted measure <span><math><mi>d</mi><mi>μ</mi><mo>=</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mi>ϕ</mi></mrow></msup><mi>d</mi><msub><mrow><mi>v</mi></mrow><mrow><mi>g</mi></mrow></msub></math></span> and diffusion operator <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>ϕ</mi></mrow></msub><mo>=</mo><msup><mrow><mi>e</mi></mrow><mrow><mi>ϕ</mi></mrow></msup><mrow><mi>div</mi></mrow><mo>(</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mi>ϕ</mi></mrow></msup><mi>∇</mi><mo>)</mo></math></span> – the <em>ϕ</em>-Laplacian. The nonlinear slow diffusion equation, then, for <span><math><mi>x</mi><mo>∈</mo><mi>M</mi></math></span> and <span><math><mi>t</mi><mo>&gt;</mo><mn>0</mn></math></span>, and fixed exponent <span><math><mi>p</mi><mo>&gt;</mo><mn>1</mn></math></span>, takes the form<span><span><span><math><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>−</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mi>ϕ</mi></mrow></msub><msup><mrow><mi>u</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>N</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>)</mo><mo>.</mo></math></span></span></span> We assume that the metric tensor <em>g</em> and potential <em>ϕ</em> are both space-time dependent; hence the same is true of the usual metric and potential dependent differential operators and curvature tensors. The estimates are established under natural lower bounds on the Bakry-Émery <em>m</em>-Ricci curvature tensor and the time derivative of metric tensor. The curious interplay between geometry, nonlinearity and evolution and their influence on the estimates is at the centre of this investigation. The results here considerably extend and improve earlier results on slow diffusion equations. Several implication, special cases and corollaries are presented and discussed.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 1","pages":"Article 129691"},"PeriodicalIF":1.2,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144134981","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":"Residually finite partial actions and MF Fell bundles","authors":"Timothy Rainone","doi":"10.1016/j.jmaa.2025.129693","DOIUrl":"10.1016/j.jmaa.2025.129693","url":null,"abstract":"<div><div>We study Blackadar and Kirchberg's matricial field (MF) property and quasidiagonality in cross-sectional <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebras constructed from Fell bundles and, in particular, from partial <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-dynamical systems. In doing so we generalize Kerr and Nowak's notion of a residually finite action to partial topological dynamical systems. We look at some examples exhibiting this property including the partial Bernoulli shift which produces an MF reduced crossed product provided the group in question is exact, residually finite, and admits an MF reduced group <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 1","pages":"Article 129693"},"PeriodicalIF":1.2,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144134980","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":"Global boundedness for an indirect consumption chemotaxis model with signal-dependent motility","authors":"Chun Wu","doi":"10.1016/j.jmaa.2025.129690","DOIUrl":"10.1016/j.jmaa.2025.129690","url":null,"abstract":"<div><div>In this paper, we consider the following chemotaxis system with signal-dependent motility and indirect signal consumption<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mrow><mo>(</mo><mi>D</mi><mo>(</mo><mi>u</mi><mo>)</mo><mi>ϕ</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>)</mo></mrow><mo>,</mo></mtd><mtd><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∈</mo><mi>Ω</mi><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>v</mi><mo>−</mo><mi>v</mi><mi>w</mi><mo>,</mo></mtd><mtd><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∈</mo><mi>Ω</mi><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>w</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>w</mi><mo>−</mo><mi>w</mi><mo>+</mo><mi>u</mi><mo>,</mo></mtd><mtd><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∈</mo><mi>Ω</mi><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> under the smooth bounded domain <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mspace></mspace><mspace></mspace><mo>(</mo><mi>n</mi><mo>≤</mo><mn>3</mn><mo>)</mo></math></span> with homogeneous Neumann boundary conditions, where the nonlinearities <span><math><mi>D</mi><mo>(</mo><mi>u</mi><mo>)</mo></math></span> and the motility function <em>ϕ</em> satisfy the following condition<span><span><span><math><mi>D</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>=</mo><msup><mrow><mo>(</mo><mi>u</mi><mo>+</mo><mi>a</mi><mo>)</mo></mrow><mrow><mi>m</mi></mrow></msup><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mtext>and</mtext><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mi>ϕ</mi><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>)</mo><mspace></mspace><mspace></mspace><mtext>is positive on</mtext><mspace></mspace><mspace></mspace><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>.</mo></math></span></span></span> It has been demonstrated that, for any sufficiently regular initial data, the associated initial-boundary value problem allows for global classical solutions. Moreover, the asymptotic behavior of the solutions is analyzed and studied.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129690"},"PeriodicalIF":1.2,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144106445","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":"Portfolio selection and consumption for individuals with truncated quadratic utilities and satiation points","authors":"Ming Zhou ,&nbsp;Shuang Li ,&nbsp;Hui Meng","doi":"10.1016/j.jmaa.2025.129686","DOIUrl":"10.1016/j.jmaa.2025.129686","url":null,"abstract":"<div><div>This paper studies the optimal life-cycle investment and consumption strategy of an agent with truncated quadratic preferences and a finite satiation point of utility, either for consumption or terminal wealth. Employing the dynamic programming and martingale methods, we derive explicit expressions for optimal policies in an unconstrained case where consumption and wealth are allowed to be negative, as well as a constrained case imposing a subsistence level for consumption and requiring that the terminal wealth must be non-negative. We allow for a general satiation point instead of taking the satiation/bliss level as the maximum point of the quadratic function. We reveal that when satiation does not occur, the lowering satiation point stimulates current consumption, while the increasing satiation point makes the risky asset more attractive. Furthermore, we demonstrate that the satiation levels of wealth and consumption are not always reached simultaneously. Interestingly, sensitivity analysis yields that wealth plays an important role in deciding the effect of mortality risk on consumption policy from a microcosmic perspective.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 1","pages":"Article 129686"},"PeriodicalIF":1.2,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144105279","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":"Invariant measure and stability for the stochastic Rayleigh-Plesset equation","authors":"Yong Chen,&nbsp;Shijie Hui,&nbsp;Daohai Du","doi":"10.1016/j.jmaa.2025.129681","DOIUrl":"10.1016/j.jmaa.2025.129681","url":null,"abstract":"<div><div>We study the stochastic Rayleigh-Plesset (RP) equation with Lévy noise in the Marcus form. We use the stochastic variational method to derive the stochastic RP equation. Then, we study the global well-posedness and the existence of the invariant measure of the stochastic RP equation. Moreover, we obtain some sufficient conditions for the stability of the stochastic RP equation. We design and test numerical methods for solving the SDE and use the equation to study the stability results.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 1","pages":"Article 129681"},"PeriodicalIF":1.2,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144105278","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":"Universal properties of spaces of generalized functions","authors":"Djameleddine Kebiche,&nbsp;Paolo Giordano","doi":"10.1016/j.jmaa.2025.129687","DOIUrl":"10.1016/j.jmaa.2025.129687","url":null,"abstract":"<div><div>Through the presentation of several examples, we motivate that universal properties are the simplest way to solve a given mathematical problem. To illustrate this point, we present the co-universal property of Schwartz distributions, as the simplest way to have derivatives of continuous functions. We also discuss Colombeau algebra as the simplest quotient algebra where representatives of zero are infinitesimal. Furthermore, we explore generalized smooth functions as the universal way to associate set-theoretical maps defined by nets of smooth functions (e.g. regularizations of distributions) and having arbitrary derivatives. Each of these properties results in a characterization up to isomorphisms of the corresponding space. The present work requires only the notions of category, functor, natural transformation and Schwartz distributions, and introduces the notion of universal solution using a simple and non-abstract language.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129687"},"PeriodicalIF":1.2,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144090561","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":"Bistability and bifurcation analysis in a viral infection model with fully coupled logistic cell growth","authors":"Shaoli Wang ,&nbsp;Wenya Zhang ,&nbsp;Yuming Chen ,&nbsp;Libin Rong","doi":"10.1016/j.jmaa.2025.129682","DOIUrl":"10.1016/j.jmaa.2025.129682","url":null,"abstract":"<div><div>In this paper, we study a delayed viral infection model that incorporates the proliferations of both healthy and infected cells, governed by fully coupled logistic growths. We begin by analyzing the dynamical behavior of the corresponding ordinary differential equation model and demonstrating its bistability, which can explain varying treatment outcomes. We then show the existence of a Hopf bifurcation in the delayed model, using the delay as the bifurcation parameter. We also classify the dynamics near the saddle-node-Hopf bifurcation point using normal form and center manifold approaches. Numerical investigations reveal the rich and complex dynamics exhibited by the models.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 1","pages":"Article 129682"},"PeriodicalIF":1.2,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144116894","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":"Spatial analyticity of solutions to quadratic nonlinear Schrödinger equations with mass resonance","authors":"Takuya Sato","doi":"10.1016/j.jmaa.2025.129684","DOIUrl":"10.1016/j.jmaa.2025.129684","url":null,"abstract":"<div><div>We consider the Cauchy problem of quadratic nonlinear Schrödinger equations in two spatial dimensions under the mass resonance condition. In this case, the problem has a critical situation in the sense of long time behavior of solutions, and a time singularity not to be integrable at <span><math><mi>t</mi><mo>=</mo><mo>∞</mo></math></span> causes from the quadratic nonlinearity. We overcome such difficulty by considering the symmetric structure of nonlinearities and prove that a unique global solution exists in a spatial analytic class with a slowly time decaying analytic radius.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129684"},"PeriodicalIF":1.2,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144105118","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":"Extending umbral calculus through (q,h)-Appell sequences","authors":"Ghazala Yasmin,&nbsp;Sanjeev Kumar","doi":"10.1016/j.jmaa.2025.129675","DOIUrl":"10.1016/j.jmaa.2025.129675","url":null,"abstract":"<div><div>The origin of <em>q</em>-analogue of Appell polynomials can be traced back to Al-Salam (1967) <span><span>[2]</span></span>, whereas the introduction of <em>h</em>-analogue as <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>h</mi></mrow></msub></math></span>-Appell sequences can be attributed to Costabile and Longo (2013) <span><span>[13]</span></span>. This article unifies these two analogues of the Appell sequences within a proposed <span><math><mo>(</mo><mi>q</mi><mo>,</mo><mi>h</mi><mo>)</mo></math></span>-umbral calculus framework. We introduce <span><math><mo>(</mo><mi>q</mi><mo>,</mo><mi>h</mi><mo>)</mo></math></span>-Appell sequences by extending standard results of umbral algebra to its <span><math><mo>(</mo><mi>q</mi><mo>,</mo><mi>h</mi><mo>)</mo></math></span>-analogue. Distinctive properties of <span><math><mo>(</mo><mi>q</mi><mo>,</mo><mi>h</mi><mo>)</mo></math></span>-Appell sequences, including generating function, conjugate representation, <span><math><mo>(</mo><mi>q</mi><mo>,</mo><mi>h</mi><mo>)</mo></math></span>-Appell identity, <span><math><mo>(</mo><mi>q</mi><mo>,</mo><mi>h</mi><mo>)</mo></math></span>-Appell characterizations, and <span><math><mo>(</mo><mi>q</mi><mo>,</mo><mi>h</mi><mo>)</mo></math></span>-Appell expansions are obtained by utilizing the norm, determinant, <span><math><mo>(</mo><mi>q</mi><mo>,</mo><mi>h</mi><mo>)</mo></math></span>-monomial, <span><math><mo>(</mo><mi>q</mi><mo>,</mo><mi>h</mi><mo>)</mo></math></span>-linear functional, and <span><math><mo>(</mo><mi>q</mi><mo>,</mo><mi>h</mi><mo>)</mo></math></span>-derivative operator. An example in the form of <span><math><mo>(</mo><mi>q</mi><mo>,</mo><mi>h</mi><mo>)</mo></math></span>-Bernoulli polynomials is also presented, along with a discussion on <span><math><mo>(</mo><mi>q</mi><mo>,</mo><mi>h</mi><mo>)</mo></math></span>-differential equations and zeros of the polynomials.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129675"},"PeriodicalIF":1.2,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144105154","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}