Journal of Mathematical Analysis and Applications最新文献

{"title":"On a class of oscillatory integrals and their application to the time dependent Schrödinger equation","authors":"J. Behrndt ,&nbsp;P. Schlosser","doi":"10.1016/j.jmaa.2024.129022","DOIUrl":"10.1016/j.jmaa.2024.129022","url":null,"abstract":"<div><div>In this paper a class of oscillatory integrals is interpreted as a limit of Lebesgue integrals with Gaussian regularizers. The convergence of the regularized integrals is shown with an improved version of iterative integration by parts that generates additional decaying factors and hence leads to better integrability properties. The general abstract results are then applied to the Cauchy problem for the one dimensional time dependent Schrödinger equation, where the solution is expressed for <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>-regular initial conditions with polynomial growth at infinity via the Green's function as an oscillatory integral.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129022"},"PeriodicalIF":1.2,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656125","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":"Infinitely many small-energy solutions of a nonlinear boundary value problem with Dirichlet-to-Neumann operator","authors":"Shaowei Chen","doi":"10.1016/j.jmaa.2024.129020","DOIUrl":"10.1016/j.jmaa.2024.129020","url":null,"abstract":"<div><div>In this study, we investigate the following nonlinear boundary value problem<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>u</mi><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></mtd><mtd><mspace></mspace><mtext>in</mtext><mspace></mspace><mi>Ω</mi></mtd></mtr><mtr><mtd><mfrac><mrow><mo>∂</mo><mi>u</mi></mrow><mrow><mo>∂</mo><mi>ν</mi></mrow></mfrac><mo>=</mo><mi>D</mi><mi>u</mi><mo>,</mo><mspace></mspace></mtd><mtd><mspace></mspace><mtext>on</mtext><mspace></mspace><mo>∂</mo><mi>Ω</mi><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> where <span><math><mn>2</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mo>+</mo><mo>∞</mo></math></span> if <span><math><mi>N</mi><mo>=</mo><mn>2</mn></math></span> and <span><math><mn>2</mn><mo>&lt;</mo><mi>p</mi><mo>≤</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> if <span><math><mi>N</mi><mo>≥</mo><mn>3</mn></math></span>, Ω is a bounded domain in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> (<span><math><mi>N</mi><mo>≥</mo><mn>2</mn></math></span>) with <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> smooth boundary, <span><math><mi>u</mi><mo>:</mo><mi>Ω</mi><mo>→</mo><mi>R</mi></math></span>, Δ<em>u</em> is the Laplacian operator, <em>ν</em> is the unit outer normal vector at ∂Ω, and <span><math><mi>D</mi></math></span> is the Dirichlet-to-Neumann operator. We prove that this equation has a sequence of solutions <span><math><mo>{</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>}</mo></math></span> that satisfies <span><math><msub><mrow><mi>lim</mi></mrow><mrow><mi>m</mi><mo>→</mo><mo>∞</mo></mrow></msub><mo>⁡</mo><msub><mrow><mo>‖</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></msub><mo>=</mo><mn>0</mn></math></span> and <span><math><msub><mrow><mrow><mi>lim</mi></mrow><mspace></mspace><mrow><mi>inf</mi></mrow></mrow><mrow><mi>m</mi><mo>→</mo><mo>∞</mo></mrow></msub><mspace></mspace><msub><mrow><mo>‖</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></msub><mo>≥</mo><mn>1</mn></math></span>. To prove this, a new critical point theorem without the usual Palais-Smale condition is used.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129020"},"PeriodicalIF":1.2,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656136","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":"Strange attractor of the Lozi mappings for the parameter region [0<b<1,b+1<a<2−b2]","authors":"Khadija Ben Rejeb","doi":"10.1016/j.jmaa.2024.129018","DOIUrl":"10.1016/j.jmaa.2024.129018","url":null,"abstract":"<div><div>In this paper, we give a mathematical proof to the existence of a strange attractor for the Lozi mapping <em>L</em>. More precisely, we prove that <em>L</em> has a unique strange attractor for the parameter region [<span><math><mn>0</mn><mo>&lt;</mo><mi>b</mi><mo>&lt;</mo><mn>1</mn><mo>,</mo><mspace></mspace><mi>b</mi><mo>+</mo><mn>1</mn><mo>&lt;</mo><mi>a</mi><mo>&lt;</mo><mn>2</mn><mo>−</mo><mfrac><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></mfrac></math></span>] which coincides with the closure of the unstable manifold at the fixed point <span><math><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>1</mn><mo>+</mo><mi>a</mi><mo>−</mo><mi>b</mi></mrow></mfrac><mo>,</mo><mfrac><mrow><mi>b</mi></mrow><mrow><mn>1</mn><mo>+</mo><mi>a</mi><mo>−</mo><mi>b</mi></mrow></mfrac><mo>)</mo></math></span>. This extends a result obtained by (M. Misiurewicz, Strange attractor for the Lozi mapping, Ann.N.Y. Acad. Sci. 357, (1980), pp. 348-358). On the other hand, we study the dynamical behavior of the map <em>L</em> on its strange attractor and we prove that it is Li-Yorke chaotic. MSC 2010 Primary: 37D45, 37E30.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129018"},"PeriodicalIF":1.2,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656135","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":"Multiplicative Hecke operators and their applications","authors":"Chang Heon Kim,&nbsp;Gyucheol Shin","doi":"10.1016/j.jmaa.2024.129002","DOIUrl":"10.1016/j.jmaa.2024.129002","url":null,"abstract":"<div><div>In this paper, we define the multiplicative Hecke operators <span><math><mi>T</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> for any positive integer on the integral weight meromorphic modular forms for <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>N</mi><mo>)</mo></math></span>. We then show that they have properties similar to those of additive Hecke operators. Moreover, we prove that multiplicative Hecke eigenforms with integer Fourier coefficients are eta quotients, and vice versa. In addition, we prove that the Borcherds product and logarithmic derivative are Hecke equivariant with the multiplicative Hecke operators and the Hecke operators on the half-integral weight harmonic weak Maass forms and weight 2 meromorphic modular forms.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129002"},"PeriodicalIF":1.2,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656177","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":"General double-sided orthogonal split quadratic phase Clifford-Fourier transform","authors":"H. Monaim ,&nbsp;M. Faress","doi":"10.1016/j.jmaa.2024.129009","DOIUrl":"10.1016/j.jmaa.2024.129009","url":null,"abstract":"<div><div>This paper provides the general double-sided orthogonal <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></math></span>-dimensional spaces split quadratic phase Clifford-Fourier transform and the general Short-time quadratic phase Clifford-Fourier transform. It proves the Rènyi and Shannon entropy and Lieb's uncertainty principles.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129009"},"PeriodicalIF":1.2,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142659061","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 diffusive predator-prey system with hunting cooperation in predators and prey-taxis: I global existence and stability","authors":"Wonlyul Ko,&nbsp;Kimun Ryu","doi":"10.1016/j.jmaa.2024.129005","DOIUrl":"10.1016/j.jmaa.2024.129005","url":null,"abstract":"<div><div>In this paper, we present and investigate a generalized reaction-diffusion system of predator-prey dynamics that incorporates prey-taxis and a hunting cooperation effect in predators, subject to homogeneous Neumann boundary conditions. This system describes a predator-prey interaction, in which the prey exhibit group defense mechanisms against their predators, and the predators cooperate to hunt these defended prey. The mechanism of prey is implemented through the (repulsive) prey-taxis term, which affects the diffusion rate of the predators, while the hunting cooperation effect of the predators towards their prey is implemented through the functional response. Moreover, this system incorporates generalized functional forms for the prey's growth rate, the predators' functional response and mortality rate, and the prey-tactic sensitivity, allowing for adaptation to various scenarios. We first establish that solutions of the time- and space-dependent system with such ecological characteristics exist globally and are bounded by estimating an associated weighted integral. Secondly, we investigate the constant coexistence state of the generalized system by introducing a constructed function that incorporates the prey's growth rate, the predators' functional response and mortality rate. Finally, we find some conditions yielding the local stability of all feasible constant and nonnegative solutions of the system, thereby revealing the occurrence of bistability. Furthermore, we conduct an investigation into the global stability at both the constant coexistence and predator-free states by applying Lyapunov stability analysis. We also analyze the rate at which the solutions to the system converge to these steady-states by utilizing the boundedness of the solutions along with Gagliardo-Nirenberg inequality.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129005"},"PeriodicalIF":1.2,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587435","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 smooth solution for the 3D generalized tropical climate model with partial viscosity and damping","authors":"Hui Liu ,&nbsp;Chengfeng Sun ,&nbsp;Mei Li","doi":"10.1016/j.jmaa.2024.129007","DOIUrl":"10.1016/j.jmaa.2024.129007","url":null,"abstract":"<div><div>The three-dimensional generalized tropical climate model with partial viscosity and damping is considered in this paper. Global well-posedness of solutions of the three-dimensional generalized tropical climate model with partial viscosity and damping is proved for <span><math><mi>α</mi><mo>≥</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span> and <span><math><mi>β</mi><mo>≥</mo><mn>4</mn></math></span>. Global smooth solution of the three-dimensional generalized tropical climate model with partial viscosity and damping is proved in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span> <span><math><mo>(</mo><mi>s</mi><mo>&gt;</mo><mn>2</mn><mo>)</mo></math></span> for <span><math><mi>α</mi><mo>≥</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span> and <span><math><mn>4</mn><mo>≤</mo><mi>β</mi><mo>≤</mo><mn>5</mn></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129007"},"PeriodicalIF":1.2,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593130","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 theorems for partial trace equations with nonlinear gradient terms","authors":"Bukayaw Kindu ,&nbsp;Ahmed Mohammed ,&nbsp;Birilew Tsegaw","doi":"10.1016/j.jmaa.2024.129010","DOIUrl":"10.1016/j.jmaa.2024.129010","url":null,"abstract":"<div><div>In this paper, we will study various Liouville-type theorems for partial trace equations with nonlinear gradient terms. Specifically, we will provide sufficient conditions for non-negative viscosity subsolutions of these equations in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> to vanish identically. For a prototype of such equations, we will give necessary and sufficient conditions for non-negative subsolutions in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> to be identically zero.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129010"},"PeriodicalIF":1.2,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587434","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":"Hypercyclicity and universality phenomena with atlas-smooth and atlas-holomorphic sequences","authors":"Thomas A. Tuberson","doi":"10.1016/j.jmaa.2024.129008","DOIUrl":"10.1016/j.jmaa.2024.129008","url":null,"abstract":"<div><div>Smooth manifolds often require one to account for multiple local coordinate systems. On a smooth manifold like real <em>n</em>-dimensional space, we typically work within a single global coordinate system. Consequently, it is not hard to define partial differentiation operators, for example, and show that they are hypercyclic. However, defining a partial differentiation operator on smooth functions defined globally on general smooth manifolds is difficult due to the multiple local coordinate systems. We introduce the concepts of atlas-smooth and atlas-holomorphic sequences, which we use to study hypercyclicity and universality on spaces of functions defined both locally and globally on manifolds. We focus on partial differentiation operators acting on smooth functions defined on smooth manifolds, and we also consider complex manifolds as well. In 1941, Seidel and Walsh <span><span>[5]</span></span> showed that a certain sequence is universal on the space of holomorphic functions defined on the open unit disk. We use the ideas developed here to extend this result to certain complex manifolds.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129008"},"PeriodicalIF":1.2,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656134","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":"Global existence and time decay rate of classical solutions to a hybrid Vlasov-Fokker-Planck-MHD equations","authors":"Peng Jiang,&nbsp;Jiayu He","doi":"10.1016/j.jmaa.2024.129004","DOIUrl":"10.1016/j.jmaa.2024.129004","url":null,"abstract":"<div><div>In this paper, we prove the existence of global classical solutions to a kinetic-fluid system when initial data is a small perturbation of some given equilibrium state in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. The system consists of the Vlasov-Fokker-Planck equation coupled with the compressible magnetohydrodynamics (MHD) equations via the nonlinear coupling terms of Lorenz force type. It describes the motion of energetic particles in a fluid with a magnetic field. The proof of global existence mainly relies on the energy method. Due to the complex nonlinear structure of Lorentz force, we need to establish a more refined uniform a prior estimates. Moreover, under additional conditions on initial data, the optimal time decay rate of solutions toward the equilibrium state can be obtained by using the Fourier analysis.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129004"},"PeriodicalIF":1.2,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593670","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}