Journal of Mathematical Analysis and Applications最新文献

{"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}

{"title":"Finite dimensional distributions for short incomplete Gauss sums","authors":"Emek Demirci Akarsu","doi":"10.1016/j.jmaa.2025.129685","DOIUrl":"10.1016/j.jmaa.2025.129685","url":null,"abstract":"<div><div>This paper investigates an equivalent principle to the weak invariance principle, with a focus on short incomplete Gauss sums. We establish a limit law for the finite-dimensional distributions (FDD) of these sums as the size parameter grows. Additionally, the study extends these findings to the limiting distribution of theta functions, building upon prior research by the author. This connection highlights the broader implications of the results in the context of homogeneous dynamics and modular forms.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129685"},"PeriodicalIF":1.2,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144090556","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":"Qualitative analysis for a two-component Camassa-Holm system with high order nonlinearity","authors":"Xuanxuan Han,&nbsp;JinRong Wang","doi":"10.1016/j.jmaa.2025.129679","DOIUrl":"10.1016/j.jmaa.2025.129679","url":null,"abstract":"<div><div>This paper is dedicated to a two-component Camassa-Holm system with high order nonlinearity, which is a multi-component extension of the Camassa-Holm equation. Firstly, the local well-posedness for the Cauchy problem of the system is established in the Sobolev-Besov spaces. Then, we construct the precise blow-up mechanism by using the transport equation theory. It is widely known that the classical methods for studying blow-up phenomena require the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm to control the velocity component. However, the system we consider no longer has the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm conservation law due to its high-order coupling property. Our approach is to utilize the fine structure of system, and then derive a new conservation law <span><math><mi>H</mi></math></span>. Furthermore, we deduce two different new blow-up results in finite time. Finally, peakon solutions are discussed as well.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129679"},"PeriodicalIF":1.2,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144083875","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":"Reducing subspaces for strictly lower triangular operators","authors":"Yanlin Liu ,&nbsp;Yufeng Lu ,&nbsp;Yanyue Shi ,&nbsp;Xiaoping Xu","doi":"10.1016/j.jmaa.2025.129683","DOIUrl":"10.1016/j.jmaa.2025.129683","url":null,"abstract":"<div><div>In this paper, we establish a lattice isomorphism between the lattice of all reducing subspaces of a strictly lower triangular operator <em>S</em> and a sublattice of certain closed subspaces of <span><math><mi>ker</mi><mo>⁡</mo><msup><mrow><mi>S</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>. Here a strictly lower triangular operator means a bounded operator <em>S</em> on a Hilbert space <em>H</em> with <span><math><msubsup><mrow><mo>∩</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow><mrow><mo>∞</mo></mrow></msubsup><mover><mrow><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>(</mo><mi>H</mi><mo>)</mo></mrow><mo>‾</mo></mover><mo>=</mo><mn>0</mn></math></span>, or equivalently, <em>S</em> possess a strictly lower triangular block matrix representation. Every unilateral operator-weighted shift is a strictly lower triangular operator. And many Toeplitz operators on function spaces are translations of strictly lower triangular operators. Further, we prove that every nonzero reducing subspace <em>X</em> of <em>S</em> satisfying <span><math><mi>dim</mi><mo>⁡</mo><mi>X</mi><mo>∩</mo><mi>ker</mi><mo>⁡</mo><msup><mrow><mi>S</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>&lt;</mo><mo>∞</mo></math></span> can be expressed as a direct sum of at most <span><math><mi>dim</mi><mo>⁡</mo><mi>X</mi><mo>∩</mo><mi>ker</mi><mo>⁡</mo><msup><mrow><mi>S</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> minimal reducing subspaces. As an application, we characterize the reducing spaces of Toeplitz operators induced by quasi-homogeneous functions on <em>n</em>-analytic Bergman space. In particular, we show that <span><math><msub><mrow><mi>T</mi></mrow><mrow><msup><mrow><mi>z</mi></mrow><mrow><mi>q</mi></mrow></msup></mrow></msub></math></span> with <span><math><mi>q</mi><mo>≥</mo><mn>1</mn></math></span> on 2-analytic Bergman space has <em>q</em> minimal reducing subspaces. Moreover, we show that the von Neumann algebra generated by the commutants of <span><math><msub><mrow><mi>T</mi></mrow><mrow><msup><mrow><mi>z</mi></mrow><mrow><mi>q</mi></mrow></msup></mrow></msub></math></span> and <span><math><msubsup><mrow><mi>T</mi></mrow><mrow><msup><mrow><mi>z</mi></mrow><mrow><mi>q</mi></mrow></msup></mrow><mrow><mo>⁎</mo></mrow></msubsup></math></span>, is ⁎-isomorphic to <span><math><msubsup><mrow><mo>⊕</mo></mrow><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>q</mi></mrow></msubsup><mi>C</mi></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129683"},"PeriodicalIF":1.2,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144083877","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":"Weighted Orlicz-Poincaré inequalities in product spaces","authors":"Lucas Yong","doi":"10.1016/j.jmaa.2025.129680","DOIUrl":"10.1016/j.jmaa.2025.129680","url":null,"abstract":"<div><div>This article is a follow-up to <span><span>[3]</span></span>. We establish necessary and sufficient conditions for weighted Orlicz-Poincaré inequalities in product spaces. These results follow the work of Chua and Wheeden <span><span>[1]</span></span>, who established similar results for weighted Poincaré inequalities in product spaces.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129680"},"PeriodicalIF":1.2,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144090560","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}