Journal of Mathematical Analysis and Applications最新文献

{"title":"Rates of convergence in the distances of Kolmogorov and Wasserstein for standardized martingales","authors":"Xiequan Fan ,&nbsp;Zhonggen Su","doi":"10.1016/j.jmaa.2025.129630","DOIUrl":"10.1016/j.jmaa.2025.129630","url":null,"abstract":"<div><div>We give some rates of convergence in the distances of Kolmogorov and Wasserstein for standardized martingales with differences having finite variances. For the Kolmogorov distances, we present some exact Berry-Esseen bounds for martingales, which generalizes some Berry-Esseen bounds due to Bolthausen. In consequence, a Lindeberg type condition for the martingale central limit theorem is obtained. For the Wasserstein distance, with Stein's method and Lindeberg's telescoping sum argument, the rates of convergence in martingale central limit theorems recover the classical rates for sums of i.i.d. random variables, and therefore they are believed to be optimal.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 1","pages":"Article 129630"},"PeriodicalIF":1.2,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143933614","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 existence of solutions for Schrödinger-Poisson equation with zero mass and a convolution nonlinearity","authors":"Xueying Tang,&nbsp;Jiuyang Wei","doi":"10.1016/j.jmaa.2025.129632","DOIUrl":"10.1016/j.jmaa.2025.129632","url":null,"abstract":"<div><div>In this article, we study the Schrödinger-Poisson system with zero mass and a convolution nonlinearity:<span><span><span><math><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn><mi>π</mi><mo>|</mo><mi>x</mi><mo>|</mo></mrow></mfrac><mo>⁎</mo><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mi>u</mi><mo>=</mo><mi>μ</mi><mo>(</mo><msub><mrow><mi>I</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>⁎</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi></mrow></msup><mo>)</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>,</mo><mspace></mspace><mspace></mspace><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo></math></span></span></span> where <span><math><mi>p</mi><mo>∈</mo><mrow><mo>(</mo><mfrac><mrow><mn>17</mn><mo>(</mo><mn>3</mn><mo>+</mo><mi>α</mi><mo>)</mo></mrow><mrow><mn>48</mn></mrow></mfrac><mo>,</mo><mn>3</mn><mo>+</mo><mi>α</mi><mo>)</mo></mrow></math></span> and <span><math><mi>μ</mi><mo>&gt;</mo><mn>0</mn></math></span>. We prove that the aforementioned system admits a ground state solution when <span><math><mi>p</mi><mo>∈</mo><mrow><mo>(</mo><mfrac><mrow><mn>17</mn><mo>(</mo><mn>3</mn><mo>+</mo><mi>α</mi><mo>)</mo></mrow><mrow><mn>48</mn></mrow></mfrac><mo>,</mo><mfrac><mrow><mn>6</mn><mo>+</mo><mi>α</mi></mrow><mrow><mn>4</mn></mrow></mfrac><mo>)</mo></mrow></math></span> or <span><math><mi>p</mi><mo>∈</mo><mrow><mo>(</mo><mfrac><mrow><mn>3</mn><mo>+</mo><mi>α</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>,</mo><mn>3</mn><mo>+</mo><mi>α</mi><mo>)</mo></mrow></math></span>; and a radially symmetric ground state solution when <span><math><mi>p</mi><mo>∈</mo><mrow><mo>(</mo><mfrac><mrow><mn>6</mn><mo>+</mo><mi>α</mi></mrow><mrow><mn>4</mn></mrow></mfrac><mo>,</mo><mfrac><mrow><mn>3</mn><mo>+</mo><mi>α</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>]</mo></mrow></math></span>. Specifically, when <span><math><mi>p</mi><mo>=</mo><mfrac><mrow><mn>6</mn><mo>+</mo><mi>α</mi></mrow><mrow><mn>4</mn></mrow></mfrac></math></span>, we demonstrate that the system only admits trivial solution for <span><math><mn>0</mn><mo>&lt;</mo><mi>μ</mi><mo>&lt;</mo><msub><mrow><mi>μ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, but admits a positive solution if <em>μ</em> takes some particular value, where <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is a specific value dependent on <em>α</em>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129632"},"PeriodicalIF":1.2,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143937197","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":"Kakutani's theorem and Ramsey sets","authors":"Andrzej Kryczka","doi":"10.1016/j.jmaa.2025.129644","DOIUrl":"10.1016/j.jmaa.2025.129644","url":null,"abstract":"<div><div>We give a short proof of Kakutani's theorem that every bounded sequence in a uniformly convex Banach space has a Cesàro summable subsequence. The proof is based on the Galvin–Prikry partition theorem on Ramsey sets.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129644"},"PeriodicalIF":1.2,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143921942","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 phase field model of Cahn–Hilliard type for tumour growth with mechanical effects and damage","authors":"Giulia Cavalleri","doi":"10.1016/j.jmaa.2025.129627","DOIUrl":"10.1016/j.jmaa.2025.129627","url":null,"abstract":"<div><div>We introduce a new diffuse interface model for tumour growth in the presence of a nutrient, in which we take into account mechanical effects and reversible tissue damage. The highly nonlinear PDEs system mainly consists of a Cahn–Hilliard type equation that describes the phase separation process between healthy and tumour tissue coupled to a parabolic reaction-diffusion equation for the nutrient and a hyperbolic equation for the balance of forces, including inertial and viscous effects. The main novelty of this work is the introduction of cellular damage, whose evolution is ruled by a parabolic differential inclusion. In this paper, we prove a global-in-time existence result for weak solutions by passing to the limit in a time-discretised and regularised version of the system.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129627"},"PeriodicalIF":1.2,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143937200","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":"Self-similar solutions of fast-reaction limit problems with nonlinear diffusion","authors":"Elaine Crooks,&nbsp;Yini Du","doi":"10.1016/j.jmaa.2025.129636","DOIUrl":"10.1016/j.jmaa.2025.129636","url":null,"abstract":"<div><div>In this paper, we present an approach to characterising self-similar fast-reaction limits of systems with nonlinear diffusion. For appropriate initial data, in the fast-reaction limit <span><math><mi>k</mi><mo>→</mo><mo>∞</mo></math></span>, spatial segregation results in the two components of the original systems converging to the positive and negative parts of a self-similar limit profile <span><math><mi>f</mi><mo>(</mo><mi>η</mi><mo>)</mo></math></span>, where <span><math><mi>η</mi><mo>=</mo><mfrac><mrow><mi>x</mi></mrow><mrow><msqrt><mrow><mi>t</mi></mrow></msqrt></mrow></mfrac></math></span>, that satisfies one of four ordinary differential systems. The existence of these self-similar solutions of the <span><math><mi>k</mi><mo>→</mo><mo>∞</mo></math></span> limit problems is proved by using shooting methods which focus on <em>a</em>, the position of the free boundary which separates the regions where the solution is positive and where it is negative, and <em>γ</em>, the derivative of <span><math><mo>−</mo><mi>ϕ</mi><mo>(</mo><mi>f</mi><mo>)</mo></math></span> at <span><math><mi>η</mi><mo>=</mo><mi>a</mi></math></span>. The position of the free boundary gives us intuition about how one substance penetrates into the other, and for specific forms of nonlinear diffusion, the relationship between the given form of the nonlinear diffusion and the position of the free boundary is also studied.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129636"},"PeriodicalIF":1.2,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144090559","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":"Minimality criteria for rational functions over Zp","authors":"Sangtae Jeong,&nbsp;Yongjae Kwon","doi":"10.1016/j.jmaa.2025.129624","DOIUrl":"10.1016/j.jmaa.2025.129624","url":null,"abstract":"<div><div>In this paper, we characterize the minimality criteria for a rational function on <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> where the denominator possesses no zeros modulo <em>p</em>. This characterization is specifically formulated regarding the coefficients of a rational function, focusing on cases where <em>p</em> equals 2 or 3. For an arbitrary prime <span><math><mi>p</mi><mo>≥</mo><mn>5</mn></math></span>, we provide an explicit formulation of the minimality criterion for such functions, contingent on the successful determination of the prescribed minimal conditions for the reduction of <em>f</em> modulo <em>p</em>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 1","pages":"Article 129624"},"PeriodicalIF":1.2,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908202","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 the invariance of holomorphic mappings of the Hartogs domain over the minimal ball","authors":"Enchao Bi ,&nbsp;Huan Yang ,&nbsp;Qiannan Zhang","doi":"10.1016/j.jmaa.2025.129623","DOIUrl":"10.1016/j.jmaa.2025.129623","url":null,"abstract":"<div><div>In this paper, we study a family of generalized Hartogs type domain over the minimal ball, which is defined by the inequality <span><math><msup><mrow><mo>‖</mo><mi>z</mi><mo>‖</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mo>|</mo><mi>z</mi><mo>⋅</mo><mi>z</mi><mo>|</mo><mo>&lt;</mo><msup><mrow><mo>(</mo><mn>1</mn><mo>−</mo><msup><mrow><mo>‖</mo><mi>w</mi><mo>‖</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mi>p</mi></mrow></msup></math></span>, where <span><math><mo>(</mo><mi>z</mi><mo>,</mo><mi>w</mi><mo>)</mo><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>×</mo><msup><mrow><mi>C</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span>. We will show that the collection of all the holomorphic self-mappings of the Hartogs type domain over a minimal ball keeping the slice function invariant form a subgroup of the automorphism group. As an application, we can build a rigidity result for the automorphism group of the generalized Hartogs type domain over the minimal ball with <span><math><mi>p</mi><mo>=</mo><mn>1</mn></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129623"},"PeriodicalIF":1.2,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143918335","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 a critical superlinear fractional (p,q)-Kirchhoff equation","authors":"Teresa Isernia","doi":"10.1016/j.jmaa.2025.129626","DOIUrl":"10.1016/j.jmaa.2025.129626","url":null,"abstract":"<div><div>We study ground state solutions to the following fractional <span><math><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span>-Kirchhoff equation<span><span><span><math><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><msubsup><mrow><mo>[</mo><mi>u</mi><mo>]</mo></mrow><mrow><mi>s</mi><mo>,</mo><mi>p</mi></mrow><mrow><mi>p</mi></mrow></msubsup><mo>)</mo></mrow><msubsup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mi>p</mi></mrow><mrow><mi>s</mi></mrow></msubsup><mi>u</mi><mo>+</mo><mrow><mo>(</mo><mi>c</mi><mo>+</mo><mi>d</mi><msubsup><mrow><mo>[</mo><mi>u</mi><mo>]</mo></mrow><mrow><mi>s</mi><mo>,</mo><mi>q</mi></mrow><mrow><mi>q</mi></mrow></msubsup><mo>)</mo></mrow><msubsup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mi>q</mi></mrow><mrow><mi>s</mi></mrow></msubsup><mi>u</mi><mo>+</mo><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo><mrow><mo>(</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>)</mo></mrow><mspace></mspace><mo>=</mo><mi>λ</mi><mi>K</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>f</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>+</mo><mi>Q</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><msubsup><mrow><mi>q</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mspace></mspace><mtext> in </mtext><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo></math></span></span></span> where <span><math><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>&gt;</mo><mn>0</mn></math></span> are constants, <span><math><mi>λ</mi><mo>&gt;</mo><mn>0</mn></math></span> is a parameter sufficiently large, <span><math><mi>s</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>, <span><math><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mi>q</mi></math></span> and <span><math><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>&lt;</mo><mi>s</mi><mi>q</mi><mo>&lt;</mo><mn>3</mn></math></span>. Here <em>V</em> is a periodic potential, the weight functions <span><math><mi>K</mi></math></span> and <span><math><mi>Q</mi></math></span> are positive and continuous functions, and <em>f</em> is a subcritical nonlinearity that does not satisfy the Ambrosetti–Rabinowitz condition. By using appropriate variational argument, we prove the existence of ground state solutions for <em>λ</em> large.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129626"},"PeriodicalIF":1.2,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143918333","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":"Hausdorff measure and decay rate of Riesz capacity","authors":"Qiuling Fan,&nbsp;Richard S. Laugesen","doi":"10.1016/j.jmaa.2025.129625","DOIUrl":"10.1016/j.jmaa.2025.129625","url":null,"abstract":"<div><div>The decay rate of Riesz capacity as the exponent increases to the dimension of the set is shown to yield Hausdorff measure. The result applies to strongly rectifiable sets, and so in particular to submanifolds of Euclidean space. For strictly self-similar fractals, a one-sided decay estimate is found. Along the way, a purely measure theoretic proof is given for subadditivity of the reciprocal of Riesz energy.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 2","pages":"Article 129625"},"PeriodicalIF":1.2,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143918334","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 fundamental gap of a kind of two dimensional sub-elliptic operator","authors":"Hongli Sun ,&nbsp;Donghui Yang ,&nbsp;Xu Zhang","doi":"10.1016/j.jmaa.2025.129619","DOIUrl":"10.1016/j.jmaa.2025.129619","url":null,"abstract":"<div><div>This paper is concerned at the minimization fundamental gap problem for a class of two-dimensional degenerate sub-elliptic operators. We establish existence results for weak solutions, Sobolev embedding theorem and spectral theory of sub-elliptic operators. We provide the existence and characterization theorems for extremizing potentials <span><math><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> when <span><math><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> is subject to <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> norm constraint.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 1","pages":"Article 129619"},"PeriodicalIF":1.2,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143918277","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}