Applied Mathematics Letters最新文献

{"title":"Global well-posedness of the Maxwell–Landau–Lifshitz equation with spin accumulation","authors":"Xiuli Xu ,&nbsp;Xueke Pu","doi":"10.1016/j.aml.2025.109617","DOIUrl":"10.1016/j.aml.2025.109617","url":null,"abstract":"<div><div>The Maxwell–Landau–Lifshitz equation with spin accumulation is studied in the paper. We prove the existence and uniqueness of global solutions using energy estimates method in two-dimensional space.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"170 ","pages":"Article 109617"},"PeriodicalIF":2.9,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144147121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Inhomogeneity, magnetic auto-Bäcklund transformations and magnetic solitons for a generalized variable-coefficient Kraenkel-Manna-Merle system in a deformed ferrite","authors":"Xin-Yi Gao ,&nbsp;Jian-Guo Liu ,&nbsp;Gang-Wei Wang","doi":"10.1016/j.aml.2025.109615","DOIUrl":"10.1016/j.aml.2025.109615","url":null,"abstract":"<div><div>Almost all the modern electronic devices have the ferromagnetic parts. For a generalized variable-coefficient Kraenkel-Manna-Merle system in a deformed ferrite, which is a generalized variable-coefficient ultrashort wave model, this paper, around a noncharacteristic movable singular manifold, symbolically computes out two magnetic auto-Bäcklund transformations, along with two families of the magnetic soliton solutions. Those results are in their reliance on the coefficients in that system. Electrodynamical implications of our magnetic auto-Bäcklund transformations and magnetic solitons come from the follow factors: the magnetic field, magnitude of the density of saturation magnetization, magnetization density, vacuum velocity of light, gyromagnetic ratio, shape of the wave during the propagation with a very short wavelength assumed, slow time variable describing the propagation over a long time or a long distance linked to the wavelength, inhomogeneity in the ferrite measuring the bond dependence of lattice defects and the corresponding exchange effects (also known as the system deformation) as well as exchange integral between the nearest-neighbor spin-spin interaction for the ferrite. With symbolic computation, the impact of inhomogeneity on the magnetic auto-Bäcklund transformations and on the transmission of magnetic solitons is presented. On the application side, the inhomogeneity could offer the possibility to realize the ultrafast magnetization switching in certain magnetic devices. Future experiments and observations might detect some features predicted in this paper, and relevant physical insights might be expected.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109615"},"PeriodicalIF":2.9,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144240819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Balanced Euler methods for the strong approximation of stochastic Volterra integral equations","authors":"Quanwei Ren,&nbsp;Yanyan He,&nbsp;Jiayi Liu","doi":"10.1016/j.aml.2025.109613","DOIUrl":"10.1016/j.aml.2025.109613","url":null,"abstract":"<div><div>This work presents a novel class of balanced Euler methods designed for approximating stochastic Volterra integral equations. These methods aim to address certain numerical instabilities commonly encountered with the explicit Euler approach. The study derives the convergence order and stability characteristics of the proposed schemes in the mean-square sense. Additionally, a comprehensive analytical investigation of linear mean-square stability is provided, focusing on convolution test equations. Numerical experiments highlight the stability and convergence performance of the balanced Euler schemes.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"170 ","pages":"Article 109613"},"PeriodicalIF":2.9,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144106436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analyzing HIV transmission through a stochastic system with the log-normal Ornstein–Uhlenbeck process","authors":"Xinhong Zhang,&nbsp;Xue Jiao","doi":"10.1016/j.aml.2025.109616","DOIUrl":"10.1016/j.aml.2025.109616","url":null,"abstract":"<div><div>This paper establishes an AIDS model that includes both asymptomatic and symptomatic infected individuals, and we assume the transmission rate follows the log-normal Ornstein–Uhlenbeck process, which allows us to develop a stochastic model. For the stochastic model, by constructing appropriate Lyapunov functions, we derive the disease will extinct when <span><math><mrow><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>e</mi></mrow></msubsup><mo>&lt;</mo><mn>1</mn></mrow></math></span>. The critical value <span><math><mrow><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>s</mi></mrow></msubsup><mo>&gt;</mo><mn>1</mn></mrow></math></span> for existence of the stationary distribution is also obtained. Additionally, observation suggests the OU process contributes to disease persistence.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"170 ","pages":"Article 109616"},"PeriodicalIF":2.9,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144124969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fast numerical study on spatial nonuniform grids for two-dimensional fractional coupled equations with fractional Neumann boundary conditions","authors":"Jiaxue Kang,&nbsp;Wenping Fan,&nbsp;Zhenhao Lu","doi":"10.1016/j.aml.2025.109609","DOIUrl":"10.1016/j.aml.2025.109609","url":null,"abstract":"<div><div>In this paper, a study on the fast numerical analysis based on spatial nonuniform grids and inverse problem for the two-dimensional space–time fractional coupled equations with fractional Neumann boundary conditions are conducted. The second order L1<span><math><msup><mrow></mrow><mrow><mo>+</mo></mrow></msup></math></span> method combined with the Crank–Nicolson (CN) method in time and the fractional block-centered finite difference (BCFD) method based on spatial nonuniform grids in space are employed. To improve computational efficiency, a fast version fractional BCFD algorithm based on the Krylov subspace iterative methods and the spatial sum-of-exponentials (SOE) technology is also constructed. Besides, to conduct the fractional parameter identification problem for the coupled model, an efficient hybrid Black Widow Optimization and Cuckoo Search (BWOCS) algorithm is applied. Numerical example is given to verify the correctness and efficiency of the proposed methods.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"169 ","pages":"Article 109609"},"PeriodicalIF":2.9,"publicationDate":"2025-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144072693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Time-splitting Fourier spectral method for two-dimensional space fractional Schrödinger–Poisson-Xα model","authors":"Pingrui Zhang,&nbsp;Junqing Jia,&nbsp;Xiaoyun Jiang","doi":"10.1016/j.aml.2025.109610","DOIUrl":"10.1016/j.aml.2025.109610","url":null,"abstract":"<div><div>We investigate the two-dimensional space fractional Schrödinger-Poisson-X<span><math><mi>α</mi></math></span> model, which incorporates fractional Laplacian operators to generalize classical quantum mechanics. By leveraging the Strang splitting Fourier spectral method, the model is solved effectively under periodic boundary conditions, ensuring high accuracy and computational efficiency. Numerical experiments confirm the second-order temporal convergence and spectral accuracy in the spatial direction. Various numerical tests are conducted to illustrate the dynamics of the model for different fractional orders, demonstrating its capability to capture complex quantum phenomena in fractional quantum systems.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"170 ","pages":"Article 109610"},"PeriodicalIF":2.9,"publicationDate":"2025-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144098246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stationary distribution of a stochastic reaction–diffusion predator–prey model with additional food, fear effect and anti-predator behavior","authors":"Haokun Qi,&nbsp;Jiani Jin,&nbsp;Bing Liu,&nbsp;Baolin Kang","doi":"10.1016/j.aml.2025.109612","DOIUrl":"10.1016/j.aml.2025.109612","url":null,"abstract":"<div><div>The stationary distribution, as a fundamental concept in stochastic processes, is of great significance for exploring the long-term behavior and stability of populations. In this paper, a stochastic reaction–diffusion predator–prey model with additional food, fear effect and anti-predator behavior is proposed, in which the stochastic fluctuations are characterized by a Ornstein–Uhlenbeck process. We proved the existence and uniqueness of the stationary distribution of the stochastic model by constructing the Lyapunov function. Moreover, this study extends the work of Qi and Liu (2024).</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"169 ","pages":"Article 109612"},"PeriodicalIF":2.9,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144070561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Instability of standing waves for cubic nonlinear Schrödinger systems with partial confinement","authors":"Wei Wang ,&nbsp;Binhua Feng","doi":"10.1016/j.aml.2025.109614","DOIUrl":"10.1016/j.aml.2025.109614","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In this paper, we consider the strong instability of standing waves for the following cubic nonlinear Schrödinger system with partial confinement &lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;When &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, Jia, Li and Luo (Discrete Contin. Dyn. Syst. 40, 2020, 2739-2766) investigated the existence of stable standing waves. When &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/m","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"170 ","pages":"Article 109614"},"PeriodicalIF":2.9,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144098348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence of positive solution for Klein–Gordon–Maxwell system without subcritical growth and Ambrosetti–Rabinowitz conditions","authors":"Xin Sun ,&nbsp;Yu Duan ,&nbsp;Jiu Liu","doi":"10.1016/j.aml.2025.109611","DOIUrl":"10.1016/j.aml.2025.109611","url":null,"abstract":"<div><div>This article concerns the following Klein–Gordon–Maxwell system <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>u</mi><mo>−</mo><mrow><mo>(</mo><mn>2</mn><mi>ω</mi><mo>+</mo><mi>ϕ</mi><mo>)</mo></mrow><mi>ϕ</mi><mi>u</mi><mo>=</mo><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>s</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><mi>λ</mi><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>,</mo><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd><mi>Δ</mi><mi>ϕ</mi><mo>=</mo><mrow><mo>(</mo><mi>ω</mi><mo>+</mo><mi>ϕ</mi><mo>)</mo></mrow><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>where <span><math><mrow><mi>ω</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> is a constant, <span><math><mrow><mn>4</mn><mo>≤</mo><mi>s</mi><mo>&lt;</mo><mn>6</mn></mrow></math></span>, <span><math><mrow><mi>λ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> is a parameter. When <span><math><mi>f</mi></math></span> only satisfies suplinear conditions but not satisfies subcritical growth and Ambrosetti–Rabinowitz conditions, the existence of positive solution can be proved via variational methods, Moser iteration and perturbation arguments. Our result unifies both critical or supercritical cases and generalizes and improves the existing ones.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"169 ","pages":"Article 109611"},"PeriodicalIF":2.9,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144069230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Linear stability analysis of 2D incompressible MHD equations with only magnetic diffusion","authors":"Jitao Liu,&nbsp;Huning Zhang","doi":"10.1016/j.aml.2025.109600","DOIUrl":"10.1016/j.aml.2025.109600","url":null,"abstract":"<div><div>Although many physical experiments and numerical simulations show that the magnetic field can stabilize and inhibit electrically conducting fluids, whether 2D incompressible MHD equations with only magnetic diffusion develop finite time singularities or not is one of the most challenging problems and remains open. Therefore, this issue has always attracted a lot of attention of mathematicians. Due to its linearized system plays a crucial role, to deeper understand the aforesaid issue, in this paper, we make the first attempt to study its linear stability when the magnetic field close to the equilibrium state <span><math><mrow><msub><mrow><mi>e</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> in the periodic domain and ultimately proposed the linear stability condition <span><span>(1.4)</span></span>. To be more precise, we show that the solution of its linearized system will be time-asymptotically stable and converge to the equilibrium state in the algebraic rate via the method of spectral analysis, as long as the integrals in the vertical direction of initial perturbations are zeros.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"169 ","pages":"Article 109600"},"PeriodicalIF":2.9,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143941937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}