Pub Date : 2024-12-14DOI: 10.1016/j.aml.2024.109424
Mengxin Chen, Xue-Zhi Li, Canrong Tian
This paper explores the spatiotemporal dynamics of a three-component predator–prey model with prey-taxis. We mainly show the existence of the steady state bifurcation and the bifurcating solution. Of most interesting discovery is that only the repulsive type prey-taxis could establish the existence of the steady state bifurcation and spatial pattern formation of the system. There are no steady state bifurcation and spatial patterns under the attractive type prey-taxis or without prey-taxis.
{"title":"Spatiotemporal dynamics in a three-component predator–prey model","authors":"Mengxin Chen, Xue-Zhi Li, Canrong Tian","doi":"10.1016/j.aml.2024.109424","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109424","url":null,"abstract":"This paper explores the spatiotemporal dynamics of a three-component predator–prey model with prey-taxis. We mainly show the existence of the steady state bifurcation and the bifurcating solution. Of most interesting discovery is that only the repulsive type prey-taxis could establish the existence of the steady state bifurcation and spatial pattern formation of the system. There are no steady state bifurcation and spatial patterns under the attractive type prey-taxis or without prey-taxis.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"92 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142823262","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}
Pub Date : 2024-12-10DOI: 10.1016/j.aml.2024.109423
Ruijing Wang, Chunqiu Li
This paper is concerned with the retarded reaction–diffusion equation ∂tu−Δu=f(u)+G(t,ut)+h(x) in a bounded domain. We allow both the nonlinear terms f and G to be supercritical, in which case the solutions may blow up in finite time, making it difficult to obtain global estimates. Here we employ some appropriate structure conditions to deal with this problem. In particular, we establish detailed global L∞-estimates and dissipative H2-estimates for the solutions and further enhance the regularity results.
{"title":"Global [formula omitted]-estimates and dissipative [formula omitted]-estimates of solutions for retarded reaction–diffusion equations","authors":"Ruijing Wang, Chunqiu Li","doi":"10.1016/j.aml.2024.109423","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109423","url":null,"abstract":"This paper is concerned with the retarded reaction–diffusion equation <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:mrow><mml:msub><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mi>u</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">−</mml:mo><mml:mi>Δ</mml:mi><mml:mi>u</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">=</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>u</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">+</mml:mo><mml:mi>G</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">+</mml:mo><mml:mi>h</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> in a bounded domain. We allow both the nonlinear terms <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:mi>f</mml:mi></mml:math> and <mml:math altimg=\"si3.svg\" display=\"inline\"><mml:mi>G</mml:mi></mml:math> to be supercritical, in which case the solutions may blow up in finite time, making it difficult to obtain global estimates. Here we employ some appropriate structure conditions to deal with this problem. In particular, we establish detailed global <mml:math altimg=\"si6.svg\" display=\"inline\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msup></mml:math>-estimates and dissipative <mml:math altimg=\"si7.svg\" display=\"inline\"><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>-estimates for the solutions and further enhance the regularity results.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"31 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142823232","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}
Pub Date : 2024-12-09DOI: 10.1016/j.aml.2024.109422
Fengmin Ge, Fusheng Luo, Fei Xu
Density functional theory calculations involve complex nonlinear models that require iterative algorithms to obtain approximate solutions. The number of iterations directly affects the computational efficiency of the iterative algorithms. However, for complex molecular systems, classical self-consistent field iterations either do not converge, or converge slowly. To improve the efficiency of self-consistent field iterations, this paper proposes a novel acceleration algorithm, which utilizes some approximate solutions to fit the convergence trend of errors and then obtains a more accurate approximate solution through extrapolation. This novel algorithm differs from previous acceleration schemes in terms of both its ideology and form. Besides using the combination of the derived approximations, we also predict a more accurate solution based on the decreasing trend of error. The significant acceleration effect of the proposed algorithm is demonstrated through numerical examples.
{"title":"Acceleration of self-consistent field iteration for Kohn–Sham density functional theory","authors":"Fengmin Ge, Fusheng Luo, Fei Xu","doi":"10.1016/j.aml.2024.109422","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109422","url":null,"abstract":"Density functional theory calculations involve complex nonlinear models that require iterative algorithms to obtain approximate solutions. The number of iterations directly affects the computational efficiency of the iterative algorithms. However, for complex molecular systems, classical self-consistent field iterations either do not converge, or converge slowly. To improve the efficiency of self-consistent field iterations, this paper proposes a novel acceleration algorithm, which utilizes some approximate solutions to fit the convergence trend of errors and then obtains a more accurate approximate solution through extrapolation. This novel algorithm differs from previous acceleration schemes in terms of both its ideology and form. Besides using the combination of the derived approximations, we also predict a more accurate solution based on the decreasing trend of error. The significant acceleration effect of the proposed algorithm is demonstrated through numerical examples.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"17 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142823118","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}
Pub Date : 2024-12-06DOI: 10.1016/j.aml.2024.109414
Francesco Dell’Accio, Francisco Marcellán, Federico Nudo
In this paper, we present a quadrature formula on triangular domains based on a set of simplex points. This formula is defined via the constrained mock-Waldron least squares approximation. Numerical experiments validate the effectiveness of the proposed method.
{"title":"A quadrature formula on triangular domains via an interpolation-regression approach","authors":"Francesco Dell’Accio, Francisco Marcellán, Federico Nudo","doi":"10.1016/j.aml.2024.109414","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109414","url":null,"abstract":"In this paper, we present a quadrature formula on triangular domains based on a set of simplex points. This formula is defined via the constrained mock-Waldron least squares approximation. Numerical experiments validate the effectiveness of the proposed method.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"21 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142823227","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}
Pub Date : 2024-12-05DOI: 10.1016/j.aml.2024.109411
Zhenjie Niu, Biao Li
The primary purpose of this work is to consider a (2+1)-dimensional generalized KP equation via ∂̄-dressing method. Using the Fourier transform and Fourier inverse transform, we give the expression of the Green function for spatial spectral problem. Then, we choose two linear independent eigenfunctions and calculate the ∂̄ derivative, a ∂̄ problem arises naturally. Based on the symmetry of the Green function, we give a standard ∂̄ equation, and its solution is expressed by the Cauchy formula.
{"title":"Dbar-dressing method for a new [formula omitted]-dimensional generalized Kadomtsev–Petviashvili equation","authors":"Zhenjie Niu, Biao Li","doi":"10.1016/j.aml.2024.109411","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109411","url":null,"abstract":"The primary purpose of this work is to consider a <mml:math altimg=\"si6.svg\" display=\"inline\"><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>-dimensional generalized KP equation via <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:mover accent=\"true\"><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mrow><mml:mo>̄</mml:mo></mml:mrow></mml:mover></mml:math>-dressing method. Using the Fourier transform and Fourier inverse transform, we give the expression of the Green function for spatial spectral problem. Then, we choose two linear independent eigenfunctions and calculate the <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:mover accent=\"true\"><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mrow><mml:mo>̄</mml:mo></mml:mrow></mml:mover></mml:math> derivative, a <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:mover accent=\"true\"><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mrow><mml:mo>̄</mml:mo></mml:mrow></mml:mover></mml:math> problem arises naturally. Based on the symmetry of the Green function, we give a standard <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:mover accent=\"true\"><mml:mrow><mml:mi>∂</mml:mi></mml:mrow><mml:mrow><mml:mo>̄</mml:mo></mml:mrow></mml:mover></mml:math> equation, and its solution is expressed by the Cauchy formula.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"47 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142823226","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}
Pub Date : 2024-12-05DOI: 10.1016/j.aml.2024.109415
Ziheng Zhang, Ying Wang
We are interested in the following problem Δ2u+λu=g(u)inRN,∫RN|u|2dx=c,where N≥5, c>0 and λ∈R appears as a Lagrange multiplier. When g(u) satisfies a class of general mass supercritical conditions, we introduce one more constraint and consider the corresponding infimum. After showing that the new constraint is natural and verifying the compactness of the minimizing sequence, we obtain the existence of normalized ground state solutions. In this sense, the existing results are generalized and improved significantly.
{"title":"Normalized ground state solutions of the biharmonic Schrödinger equation with general mass supercritical nonlinearities","authors":"Ziheng Zhang, Ying Wang","doi":"10.1016/j.aml.2024.109415","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109415","url":null,"abstract":"We are interested in the following problem <ce:display><ce:formula><mml:math altimg=\"si1.svg\" display=\"block\"><mml:mfenced close=\"\" open=\"{\"><mml:mrow><mml:mtable align=\"axis\" columnlines=\"none\" equalcolumns=\"false\" equalrows=\"false\"><mml:mtr><mml:mtd columnalign=\"left\"><mml:msup><mml:mrow><mml:mi>Δ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi>u</mml:mi><mml:mo>+</mml:mo><mml:mi>λ</mml:mi><mml:mi>u</mml:mi><mml:mo>=</mml:mo><mml:mi>g</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>u</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mspace width=\"0.16667em\"></mml:mspace><mml:mspace width=\"0.16667em\"></mml:mspace><mml:mspace width=\"0.16667em\"></mml:mspace><mml:mspace width=\"0.16667em\"></mml:mspace><mml:mtext>in</mml:mtext><mml:mspace width=\"0.16667em\"></mml:mspace><mml:mspace width=\"0.16667em\"></mml:mspace><mml:mspace width=\"0.16667em\"></mml:mspace><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">R</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msup><mml:mo>,</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign=\"left\"><mml:msub><mml:mrow><mml:mo linebreak=\"badbreak\">∫</mml:mo></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">R</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:msub><mml:msup><mml:mrow><mml:mrow><mml:mo>|</mml:mo><mml:mi>u</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi>d</mml:mi><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:mi>c</mml:mi><mml:mo>,</mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mfenced></mml:math></ce:formula></ce:display>where <mml:math altimg=\"si4.svg\" display=\"inline\"><mml:mrow><mml:mi>N</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">≥</mml:mo><mml:mn>5</mml:mn></mml:mrow></mml:math>, <mml:math altimg=\"si5.svg\" display=\"inline\"><mml:mrow><mml:mi>c</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">></mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math> and <mml:math altimg=\"si6.svg\" display=\"inline\"><mml:mrow><mml:mi>λ</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">∈</mml:mo><mml:mi mathvariant=\"double-struck\">R</mml:mi></mml:mrow></mml:math> appears as a Lagrange multiplier. When <mml:math altimg=\"si7.svg\" display=\"inline\"><mml:mrow><mml:mi>g</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>u</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> satisfies a class of general mass supercritical conditions, we introduce one more constraint and consider the corresponding infimum. After showing that the new constraint is natural and verifying the compactness of the minimizing sequence, we obtain the existence of normalized ground state solutions. In this sense, the existing results are generalized and improved significantly.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"17 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142790137","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}
Pub Date : 2024-12-04DOI: 10.1016/j.aml.2024.109412
HuanHuan Qiu, Beijia Ren, Rong Zou
In this paper, we establish the global stability of the spatially nonhomogeneous steady state solution of a reaction diffusion equation with nonlocal delay under the Dirichlet boundary condition. To achieve this, we obtain the global existence and nonnegativity of solutions and give an extensive study on the properties of omega limit sets.
{"title":"Global stability of reaction–diffusion equation with nonlocal delay","authors":"HuanHuan Qiu, Beijia Ren, Rong Zou","doi":"10.1016/j.aml.2024.109412","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109412","url":null,"abstract":"In this paper, we establish the global stability of the spatially nonhomogeneous steady state solution of a reaction diffusion equation with nonlocal delay under the Dirichlet boundary condition. To achieve this, we obtain the global existence and nonnegativity of solutions and give an extensive study on the properties of omega limit sets.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"6 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142823228","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}
Pub Date : 2024-12-04DOI: 10.1016/j.aml.2024.109413
Ning Bai, Rui Xu
Existing studies have shown that asymptomatic cases might be related to short-term immunity on a timescale of weeks to months, which could have a significant impact on cholera epidemic transmission. In this paper, we are concerned with the global dynamical behavior of a cholera model with temporary immunity, which is characterized by discrete delay. The basic reproduction number of the model and the existence of each of feasible equilibria are studied. By using an iteration technique and comparison argument, sufficient conditions are obtained for the global attractivity of the endemic equilibrium.
{"title":"Global dynamical behavior of a cholera model with temporary immunity","authors":"Ning Bai, Rui Xu","doi":"10.1016/j.aml.2024.109413","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109413","url":null,"abstract":"Existing studies have shown that asymptomatic cases might be related to short-term immunity on a timescale of weeks to months, which could have a significant impact on cholera epidemic transmission. In this paper, we are concerned with the global dynamical behavior of a cholera model with temporary immunity, which is characterized by discrete delay. The basic reproduction number of the model and the existence of each of feasible equilibria are studied. By using an iteration technique and comparison argument, sufficient conditions are obtained for the global attractivity of the endemic equilibrium.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"22 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142823230","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}
Alzheimer’s disease (AD) is characterized by the progressive deposition of β-amyloid (Aβ) plaques in the brain, where the Aβ oligomers have been confirmed to produce the critical cytotoxicity during the disease process. In this study, a model is established to describe the effect of Aβ oligomers on the interplay between Aβ and Ca2＋. Mathematical analysis demonstrates the existence and stability of the equilibria and the conditions under which backward bifurcation and saddle–node bifurcation occur are proposed. In addition, the aggregate reproduction number R0 is introduced to characterize the progression of AD. These results may offer valuable insights for studying AD-related medical strategies.
{"title":"A study in Alzheimer’s disease model for pathological effect of oligomers on the interplay between [formula omitted]-amyloid and Ca2＋","authors":"Mingyan Dong, Yongxin Zhang, Gui-Quan Sun, Zun-Guang Guo, Jiao Zhang","doi":"10.1016/j.aml.2024.109407","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109407","url":null,"abstract":"Alzheimer’s disease (AD) is characterized by the progressive deposition of <mml:math altimg=\"si7.svg\" display=\"inline\"><mml:mi>β</mml:mi></mml:math>-amyloid (A<mml:math altimg=\"si7.svg\" display=\"inline\"><mml:mi>β</mml:mi></mml:math>) plaques in the brain, where the A<mml:math altimg=\"si7.svg\" display=\"inline\"><mml:mi>β</mml:mi></mml:math> oligomers have been confirmed to produce the critical cytotoxicity during the disease process. In this study, a model is established to describe the effect of A<mml:math altimg=\"si7.svg\" display=\"inline\"><mml:mi>β</mml:mi></mml:math> oligomers on the interplay between A<mml:math altimg=\"si7.svg\" display=\"inline\"><mml:mi>β</mml:mi></mml:math> and Ca<ce:sup loc=\"post\">2＋</ce:sup>. Mathematical analysis demonstrates the existence and stability of the equilibria and the conditions under which backward bifurcation and saddle–node bifurcation occur are proposed. In addition, the aggregate reproduction number <mml:math altimg=\"si6.svg\" display=\"inline\"><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math> is introduced to characterize the progression of AD. These results may offer valuable insights for studying AD-related medical strategies.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"54 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142790149","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}
Pub Date : 2024-11-30DOI: 10.1016/j.aml.2024.109410
Qian Wang
The classical Haddock conjecture is extended to a kind of non-autonomous neutral functional differential equations (NFDEs) incorporating time-varying delays in this paper. By using the Dini derivative theory and inequality analyses, without requiring the strictly monotonically increasing property of the delay feedback function, it is demonstrated that every solution of the considered NFDEs is bounded and converges to a constant, which fully refines and generalizes the existing findings.
{"title":"New asymptotic study on the non-autonomous NFDEs involving Haddock conjecture","authors":"Qian Wang","doi":"10.1016/j.aml.2024.109410","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109410","url":null,"abstract":"The classical Haddock conjecture is extended to a kind of non-autonomous neutral functional differential equations (NFDEs) incorporating time-varying delays in this paper. By using the Dini derivative theory and inequality analyses, without requiring the strictly monotonically increasing property of the delay feedback function, it is demonstrated that every solution of the considered NFDEs is bounded and converges to a constant, which fully refines and generalizes the existing findings.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"33 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142790148","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}
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