Journal of Mathematical Analysis and Applications最新文献

{"title":"Chaos for endomorphisms of completely metrizable groups and linear operators on Fréchet spaces","authors":"Zhen Jiang,&nbsp;Jian Li","doi":"10.1016/j.jmaa.2024.129033","DOIUrl":"10.1016/j.jmaa.2024.129033","url":null,"abstract":"<div><div>Using some techniques from topological dynamics, we give a uniform treatment of Li-Yorke chaos, mean Li-Yorke chaos and distributional chaos for continuous endomorphisms of completely metrizable groups, and characterize three kinds of chaos (resp. extreme chaos) in terms of the existence of the so-called semi-irregular points (resp. irregular points). We exhibit some examples of inner automorphisms of Polish groups to illustrate the results. We also apply our results to the chaos theory of continuous linear operators on Fréchet spaces, which improves some results in the literature.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129033"},"PeriodicalIF":1.2,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656122","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":"Quantitative uniqueness of solutions to a class of Schrödinger equations with inverse square potentials","authors":"Xiujin Chen ,&nbsp;Hairong Liu","doi":"10.1016/j.jmaa.2024.129032","DOIUrl":"10.1016/j.jmaa.2024.129032","url":null,"abstract":"<div><div>This paper is devoted to proving the quantitative unique continuation property for solutions to a class of Schrödinger equations with inverse square potentials. The argument is to introduce a frequency function and show an almost monotonicity formula and three-ball inequalities by combining the Hardy's inequality.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129032"},"PeriodicalIF":1.2,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656180","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 two-lane bidirectional nonlocal traffic model","authors":"Harold Deivi Contreras ,&nbsp;Paola Goatin ,&nbsp;Luis-Miguel Villada","doi":"10.1016/j.jmaa.2024.129027","DOIUrl":"10.1016/j.jmaa.2024.129027","url":null,"abstract":"<div><div>We propose and study a nonlocal system of balance laws, which models the traffic dynamics on a two-lane and two-way road where drivers have a preferred lane (the lane on their right) and the other one is used only for overtaking. In this model, the convective part is intended to describe the intralane dynamics of vehicles: the flux function includes local and nonlocal terms, namely, the velocity function in each lane depends locally on the density of the class of vehicles traveling on their preferred lane and in a nonlocal form on the density of the class of vehicles overtaking in the opposite direction. The source terms are intended to describe the coupling between the two lanes: the overtaking and return criteria depend on weighted means of the downstream traffic density of the class of vehicles traveling in their preferred lane and of the class of vehicles traveling in the opposite direction on the same lane. We construct approximate solutions using a finite volume scheme and we prove existence of weak solutions by means of compactness estimates. We also show some numerical simulations to describe the behavior of the numerical solutions in different situations and to illustrate some features of model.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129027"},"PeriodicalIF":1.2,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656126","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":"Lump and interaction solutions to a (3+1)-dimensional BKP-Boussinesq-like equation","authors":"Xiyan Yang,&nbsp;Liangping Tang,&nbsp;Xinyi Gu,&nbsp;Wenxia Chen,&nbsp;Lixin Tian","doi":"10.1016/j.jmaa.2024.129030","DOIUrl":"10.1016/j.jmaa.2024.129030","url":null,"abstract":"<div><div>This paper analyzes the (3+1)-dimensional BKP-Boussinesq-like equation, which is widely used to describe and understand nonlinear wave phenomena. We extend Hirota's bilinear method and obtain the generalized bilinear operator. When the prime number <span><math><mi>p</mi><mo>=</mo><mn>3</mn></math></span>, the generalized bilinear form of BKP-Boussinesq-like equation is constructed. Based on its bilinear expression, we explore the lump and lump-soliton solutions to the equation, and analyze the dynamic characteristics and properties of soliton solutions with plots.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129030"},"PeriodicalIF":1.2,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587093","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":"Closed-form formulas of two Gauss hypergeometric functions of specific parameters","authors":"Gradimir V. Milovanović ,&nbsp;Feng Qi","doi":"10.1016/j.jmaa.2024.129024","DOIUrl":"10.1016/j.jmaa.2024.129024","url":null,"abstract":"<div><div>Using the Faà di Bruno formula, along with three identities of the partial Bell polynomials, and leveraging two differentiation formulas for the Gauss hypergeometric functions, the authors present several closed-form formulas for the Gauss hypergeometric functions<span><span><span><math><mmultiscripts><mrow><mi>F</mi></mrow><mrow><mn>1</mn></mrow><none></none><mprescripts></mprescripts><mrow><mn>2</mn></mrow><none></none></mmultiscripts><mo>(</mo><mi>n</mi><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>,</mo><mi>n</mi><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>;</mo><mi>n</mi><mo>+</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>;</mo><mo>−</mo><msup><mrow><mi>z</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mspace></mspace><mtext>and</mtext><mspace></mspace><mmultiscripts><mrow><mi>F</mi></mrow><mrow><mn>1</mn></mrow><none></none><mprescripts></mprescripts><mrow><mn>2</mn></mrow><none></none></mmultiscripts><mo>(</mo><mn>1</mn><mo>,</mo><mi>n</mi><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>;</mo><mi>n</mi><mo>+</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>;</mo><msup><mrow><mi>z</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span></span></span> for <span><math><mi>n</mi><mo>∈</mo><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>}</mo></math></span> and <span><math><mo>|</mo><mi>z</mi><mo>|</mo><mo>&lt;</mo><mn>1</mn></math></span>. These formulas are analyzed in light of three Gauss relations for contiguous functions, with the aid of a relation between the Gauss hypergeometric functions and the Lerch transcendent. Additionally, the authors determine the location and distribution of the zeros of two polynomials involved in these representations, which contain generalized binomial coefficients. By comparing these formulas, they also derive several combinatorial identities.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129024"},"PeriodicalIF":1.2,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656178","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":"Liouville-type theorem for higher order Hardy-Hénon type systems on the sphere","authors":"Rong Zhang ,&nbsp;Vishvesh Kumar ,&nbsp;Michael Ruzhansky","doi":"10.1016/j.jmaa.2024.129029","DOIUrl":"10.1016/j.jmaa.2024.129029","url":null,"abstract":"<div><div>In this paper, we study Liouville type theorems for the positive solutions to the following higher order Hardy-Hénon type system involving the conformal GJMS operator on the sphere <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. In order to study this we first employ the Mobius transform to transform the above Hardy-Hénon type system on the sphere <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> into a higher order elliptic system on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. Then, we show that every positive solution of the higher order elliptic system on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> is a solution to the associated integral system on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> by using polyharmonic average and iteration arguments. We use the method of moving planes in integral form to prove that there are no positive solutions for the integral system on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. Finally, together with the symmetry of the sphere <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, we obtain the Liouville type theorem of the higher order Hardy-Hénon type system involving the GJMS operator on the sphere. The results of this paper are also new even for the Lane-Emden system on the sphere.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129029"},"PeriodicalIF":1.2,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656179","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":"Bergman spaces for the bicomplex Vekua equation with bounded coefficients","authors":"Víctor A. Vicente-Benítez","doi":"10.1016/j.jmaa.2024.129025","DOIUrl":"10.1016/j.jmaa.2024.129025","url":null,"abstract":"<div><div>We develop the theory for the Bergman spaces of generalized <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-solutions of the bicomplex-Vekua equation <span><math><mover><mrow><mo>∂</mo></mrow><mo>‾</mo></mover><mi>W</mi><mo>=</mo><mi>a</mi><mi>W</mi><mo>+</mo><mi>b</mi><mover><mrow><mi>W</mi></mrow><mo>‾</mo></mover></math></span> on bounded domains, where the coefficients <em>a</em> and <em>b</em> are bounded bicomplex-valued functions. We study the completeness of the Bergman space, the regularity of the solutions, and the boundedness of the evaluation functional. For the case <span><math><mi>p</mi><mo>=</mo><mn>2</mn></math></span>, the existence of a reproducing kernel is established, along with a representation of the orthogonal projection onto the Bergman space in terms of the obtained reproducing kernel, and an explicit expression for the orthogonal complement. Additionally, we analyze the main Vekua equation (<span><math><mi>a</mi><mo>=</mo><mn>0</mn></math></span>, <span><math><mi>b</mi><mo>=</mo><mfrac><mrow><mover><mrow><mo>∂</mo></mrow><mo>‾</mo></mover><mi>f</mi></mrow><mrow><mi>f</mi></mrow></mfrac></math></span> with <em>f</em> being a non-vanishing complex-valued function). Results concerning its relationship with a pair of conductivity equations, the construction of metaharmonic conjugates, and the Runge property are presented.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129025"},"PeriodicalIF":1.2,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656118","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 Riemann-Liouville fractional integral in Bochner-Lebesgue spaces III","authors":"Paulo M. Carvalho-Neto ,&nbsp;Renato Fehlberg Júnior","doi":"10.1016/j.jmaa.2024.129023","DOIUrl":"10.1016/j.jmaa.2024.129023","url":null,"abstract":"<div><div>In this manuscript, we examine the continuity properties of the Riemann-Liouville fractional integral for order <span><math><mi>α</mi><mo>=</mo><mn>1</mn><mo>/</mo><mi>p</mi></math></span>, where <span><math><mi>p</mi><mo>&gt;</mo><mn>1</mn></math></span>, mapping from <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>;</mo><mi>X</mi><mo>)</mo></math></span> to the Banach space <span><math><mi>B</mi><mi>M</mi><mi>O</mi><mo>(</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>;</mo><mi>X</mi><mo>)</mo><mo>∩</mo><msub><mrow><mi>K</mi></mrow><mrow><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>/</mo><mi>p</mi></mrow></msub><mo>(</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>;</mo><mi>X</mi><mo>)</mo></math></span>. This improvement, refines a result by Hardy-Littlewood. To achieve this, we study properties between spaces <span><math><mi>B</mi><mi>M</mi><mi>O</mi><mo>(</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>;</mo><mi>X</mi><mo>)</mo></math></span> and <span><math><msub><mrow><mi>K</mi></mrow><mrow><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>/</mo><mi>p</mi></mrow></msub><mo>(</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>;</mo><mi>X</mi><mo>)</mo></math></span>. Additionally, we obtained the boundedness of the fractional integral of order <span><math><mi>α</mi><mo>≥</mo><mn>1</mn></math></span> from <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>;</mo><mi>X</mi><mo>)</mo></math></span> into the Riemann-Liouville fractional Sobolev space <span><math><msubsup><mrow><mi>W</mi></mrow><mrow><mi>R</mi><mi>L</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>p</mi></mrow></msubsup><mo>(</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>;</mo><mi>X</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129023"},"PeriodicalIF":1.2,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656121","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":"Isometries on Tsirelson-type spaces","authors":"A. Golbaharan ,&nbsp;S. Amiri","doi":"10.1016/j.jmaa.2024.129019","DOIUrl":"10.1016/j.jmaa.2024.129019","url":null,"abstract":"<div><div>We provide a characterization of the surjective linear isometries on certain sequence spaces that follow the Tsirelson norm.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129019"},"PeriodicalIF":1.2,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593129","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 numerical radius of weighted shift operators with generalized geometric weights","authors":"Bikshan Chakraborty,&nbsp;Sarita Ojha","doi":"10.1016/j.jmaa.2024.129021","DOIUrl":"10.1016/j.jmaa.2024.129021","url":null,"abstract":"<div><div>In this paper, we give bounds on the numerical radius of the weighted shift operator <em>T</em> with generalized geometric weights<span><span><span><math><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mi>s</mi><mi>q</mi><mo>,</mo><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mi>s</mi><msup><mrow><mi>q</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo><mo>…</mo><mo>,</mo><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn><mi>n</mi><mo>−</mo><mn>2</mn></mrow></msup><mo>,</mo><mi>s</mi><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>,</mo><mo>…</mo><mo>)</mo></mrow><mo>,</mo></math></span></span></span> where <span><math><mi>s</mi><mo>&gt;</mo><mn>0</mn></math></span> and <span><math><mn>0</mn><mo>&lt;</mo><mi>q</mi><mo>&lt;</mo><mn>1</mn></math></span>. Also, we provide the entire function <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></span> whose minimal positive root gives the numerical radius of the weighted shift operator <em>T</em>. The purpose of this paper is to generalize the results of numerical radius for the weighted shift operator with geometric weights given in <span><span>[5]</span></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129021"},"PeriodicalIF":1.2,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656123","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}