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The first eigenvalue of polyharmonic operators and its applications
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-04-01 DOI: 10.1016/j.aml.2025.109559
Meiqiang Feng, Yichen Lu
{"title":"The first eigenvalue of polyharmonic operators and its applications","authors":"Meiqiang Feng,&nbsp;Yichen Lu","doi":"10.1016/j.aml.2025.109559","DOIUrl":"10.1016/j.aml.2025.109559","url":null,"abstract":"<div><div>In this paper, our main purpose is to prove the existence of the first eigenvalue for the polyharmonic operator with Navier boundary conditions. In addition, the corresponding eigenfunction is demonstrated to be positive. As an application, we will discuss a necessary condition for the existence of positive solutions to some polyharmonic problems on the first eigenvalue.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"167 ","pages":"Article 109559"},"PeriodicalIF":2.9,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761338","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}
引用次数: 0
Asymptotic profile of steady states for a partially degenerate Aedes aegypti population model
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-03-30 DOI: 10.1016/j.aml.2025.109554
Jie Xing, Hua Nie
{"title":"Asymptotic profile of steady states for a partially degenerate Aedes aegypti population model","authors":"Jie Xing,&nbsp;Hua Nie","doi":"10.1016/j.aml.2025.109554","DOIUrl":"10.1016/j.aml.2025.109554","url":null,"abstract":"<div><div>This paper explores the asymptotic profile of steady states in a partially degenerate Aedes aegypti population model within advective environments. By reducing the model to a scalar equation, we establish the existence and uniqueness of positive steady-state solutions using the method of upper and lower solutions. We analyze the interaction between diffusion and advection, focusing on their effects on the species’ spatial distribution. Specifically, we examine how variations in diffusion and advection rates impact the asymptotic profiles. Our results show that high advection rates and low diffusion rates lead to species concentration downstream. These findings provide important insights into Aedes aegypti population dynamics in bounded domains, highlighting the critical roles of advection and diffusion in shaping spatial patterns of the species.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"167 ","pages":"Article 109554"},"PeriodicalIF":2.9,"publicationDate":"2025-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761328","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}
引用次数: 0
Conservative Crank–Nicolson-type and compact finite difference schemes for modeling the Schrödinger equation with point nonlinearity
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-03-28 DOI: 10.1016/j.aml.2025.109553
Yong Wu , Fenghua Tong , Xuanxuan Zhou , Yongyong Cai
{"title":"Conservative Crank–Nicolson-type and compact finite difference schemes for modeling the Schrödinger equation with point nonlinearity","authors":"Yong Wu ,&nbsp;Fenghua Tong ,&nbsp;Xuanxuan Zhou ,&nbsp;Yongyong Cai","doi":"10.1016/j.aml.2025.109553","DOIUrl":"10.1016/j.aml.2025.109553","url":null,"abstract":"<div><div>In this paper, we propose conservative Crank–Nicolson-type and compact finite difference schemes for the nonlinear Schrödinger equation with point nonlinearity. To construct these schemes, we first transform the point nonlinearity into an interface condition, then decompose the computational domain along the interface into two subregions with a jump condition. Different discretization approximations of the jump condition lead to different numerical schemes. For the Crank–Nicolson finite difference scheme, we prove its unconditional mass conservation and energy conservation. Some numerical examples are also presented to illustrate the accuracy and efficiency of our proposed schemes.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"167 ","pages":"Article 109553"},"PeriodicalIF":2.9,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761329","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}
引用次数: 0
A preconditioning technique of Gauss–Legendre quadrature for the logarithm of symmetric positive definite matrices
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-03-25 DOI: 10.1016/j.aml.2025.109552
Fuminori Tatsuoka, Tomohiro Sogabe, Tomoya Kemmochi, Shao-Liang Zhang
{"title":"A preconditioning technique of Gauss–Legendre quadrature for the logarithm of symmetric positive definite matrices","authors":"Fuminori Tatsuoka,&nbsp;Tomohiro Sogabe,&nbsp;Tomoya Kemmochi,&nbsp;Shao-Liang Zhang","doi":"10.1016/j.aml.2025.109552","DOIUrl":"10.1016/j.aml.2025.109552","url":null,"abstract":"<div><div>This note considers the computation of the logarithm of symmetric positive definite matrices using the Gauss–Legendre (GL) quadrature. The GL quadrature becomes slow when the condition number of the given matrix is large. In this note, we propose a technique dividing the matrix logarithm into two matrix logarithms, where the condition numbers of the divided logarithm arguments are smaller than that of the original matrix. Although the matrix logarithm needs to be computed twice, each computation can be performed more efficiently, and it potentially reduces the overall computational cost. It is shown that the proposed technique is effective when the condition number of the given matrix is approximately between 130 and <span><math><mrow><mn>3</mn><mo>.</mo><mn>0</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>5</mn></mrow></msup></mrow></math></span>.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"167 ","pages":"Article 109552"},"PeriodicalIF":2.9,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143714660","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}
引用次数: 0
On absolute value equations associated with M-matrices and H-matrices
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-03-19 DOI: 10.1016/j.aml.2025.109550
Chun-Hua Guo
{"title":"On absolute value equations associated with M-matrices and H-matrices","authors":"Chun-Hua Guo","doi":"10.1016/j.aml.2025.109550","DOIUrl":"10.1016/j.aml.2025.109550","url":null,"abstract":"<div><div>We consider the absolute value equation (AVE) <span><math><mrow><mi>A</mi><mi>x</mi><mo>−</mo><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow><mo>=</mo><mi>b</mi></mrow></math></span>, where the diagonal entries of <span><math><mrow><mi>A</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow></msup></mrow></math></span> are all greater than 1 and <span><math><mrow><mrow><mo>〈</mo><mi>A</mi><mo>〉</mo></mrow><mo>−</mo><mi>I</mi></mrow></math></span> is an irreducible singular <span><math><mi>M</mi></math></span>-matrix (<span><math><mrow><mo>〈</mo><mi>A</mi><mo>〉</mo></mrow></math></span> is the comparison matrix of <span><math><mi>A</mi></math></span>). We investigate the existence and uniqueness of solutions for the AVE. The AVE does not necessarily have a unique solution for every <span><math><mrow><mi>b</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></math></span>, so most of the existing convergence results for various iterative methods are not generally applicable. Moreover, the generalized Newton method may break down. We show that if the AVE has a solution <span><math><msup><mrow><mi>x</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> with at least one negative component, then the sequence generated by the generalized Gauss–Seidel iteration converges to <span><math><msup><mrow><mi>x</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> linearly for any initial vector.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109550"},"PeriodicalIF":2.9,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143675633","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}
引用次数: 0
On the linear independence condition for the Bobkov-Tanaka first eigenvalue of the double-phase operator
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-03-19 DOI: 10.1016/j.aml.2025.109549
Nirjan Biswas , Laura Gambera , Umberto Guarnotta
{"title":"On the linear independence condition for the Bobkov-Tanaka first eigenvalue of the double-phase operator","authors":"Nirjan Biswas ,&nbsp;Laura Gambera ,&nbsp;Umberto Guarnotta","doi":"10.1016/j.aml.2025.109549","DOIUrl":"10.1016/j.aml.2025.109549","url":null,"abstract":"<div><div>The paper investigates a pivotal condition for the Bobkov-Tanaka type spectrum for double-phase operators. This condition is satisfied if either the weight <span><math><mi>w</mi></math></span> driving the double-phase operator is strictly positive in the whole domain or the domain is convex and fulfils a suitable symmetry condition.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109549"},"PeriodicalIF":2.9,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143675634","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}
引用次数: 0
Asymptotical stability of a stochastic SIQRS epidemic model with log-normal Ornstein–Uhlenbeck process
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-03-19 DOI: 10.1016/j.aml.2025.109551
Xiao Li, Qun Liu
{"title":"Asymptotical stability of a stochastic SIQRS epidemic model with log-normal Ornstein–Uhlenbeck process","authors":"Xiao Li,&nbsp;Qun Liu","doi":"10.1016/j.aml.2025.109551","DOIUrl":"10.1016/j.aml.2025.109551","url":null,"abstract":"<div><div>In this work, we propose and analyze a stochastic SIQRS epidemic model with the disease transmission rate driven by a log-normal Ornstein–Uhlenbeck process. By establishing a series of Lyapunov functions, we derive sufficient criteria for the asymptotical stability of the positive equilibrium of the system which suggests the prevalence of the disease in the long term. This work provides a basis for taking measures to control the disease dynamics.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109551"},"PeriodicalIF":2.9,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143675608","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}
引用次数: 0
Global dynamics of a two-stage social insect model incorporating nonlinear egg cannibalism
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-03-19 DOI: 10.1016/j.aml.2025.109533
Tao Feng, Xinyu Wu
{"title":"Global dynamics of a two-stage social insect model incorporating nonlinear egg cannibalism","authors":"Tao Feng,&nbsp;Xinyu Wu","doi":"10.1016/j.aml.2025.109533","DOIUrl":"10.1016/j.aml.2025.109533","url":null,"abstract":"<div><div>This study refines the two-stage social insect model of Kang et al. (2015) by incorporating a nonlinear egg cannibalism rate. The introduction of nonlinearity presents analytical challenges, addressed through the application of the compound matrix method to rigorously establish global stability. The analysis reveals complex dynamical behaviors, including two distinct types of bistability: one between extinction and coexistence equilibria, and another between low-density and high-density coexistence equilibria. These findings underscore the ecological importance of nonlinear egg cannibalism in shaping population dynamics and enhancing species persistence under resource-limited conditions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109533"},"PeriodicalIF":2.9,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143675635","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}
引用次数: 0
Eigenvalue problems with unbalanced growth
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-03-18 DOI: 10.1016/j.aml.2025.109548
Nejmeddine Chorfi , Nikolaos S. Papageorgiou , Vicenţiu D. Rădulescu
{"title":"Eigenvalue problems with unbalanced growth","authors":"Nejmeddine Chorfi ,&nbsp;Nikolaos S. Papageorgiou ,&nbsp;Vicenţiu D. Rădulescu","doi":"10.1016/j.aml.2025.109548","DOIUrl":"10.1016/j.aml.2025.109548","url":null,"abstract":"<div><div>We consider a nonlinear eigenvalue problem driven by the nonautonomous <span><math><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></math></span>-Laplacian with unbalanced growth. Using suitable Rayleigh quotients and variational tools, we show that the problem has a continuous spectrum which is an upper half line and we also show a nonexistence result for a lower half line.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109548"},"PeriodicalIF":2.9,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143675636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the decay rate for a stochastic delay differential equation with an unbounded delay
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-03-11 DOI: 10.1016/j.aml.2025.109541
Xin Yao , Surong You , Wei Mao , Xuerong Mao
{"title":"On the decay rate for a stochastic delay differential equation with an unbounded delay","authors":"Xin Yao ,&nbsp;Surong You ,&nbsp;Wei Mao ,&nbsp;Xuerong Mao","doi":"10.1016/j.aml.2025.109541","DOIUrl":"10.1016/j.aml.2025.109541","url":null,"abstract":"<div><div>How does the delay function affect its decay rate for a stable stochastic delay differential equation with an unbounded delay? Under suitable Khasminskii-type conditions, an existence-and-uniqueness theorem for an SDDE with a general unbounded time-varying delay will be firstly given. Its decay rate will be discussed when the equation is stable. Given the unbounded delay function, it will be shown that the decay rate can be directly expressed as a function of the delay.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109541"},"PeriodicalIF":2.9,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143610324","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}
引用次数: 0
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