We study the existence of infinitely many sign-changing solutions to the following nonlinear scalar Schrödinger equation with a prescribed mass Here , is a given constant and is an unknown parameter appearing as a Lagrange multiplier. Jeanjean and Lu have established the existence of infinitely many sign-changing normalized solutions in [Nonlinearity 32 (2019), no. 12, 4942–4966] and [Calc. Var. Partial Differential Equations 59 (2020), no. 5, Paper No. 174, 43 pp.] for or . After fully utilizing the properties of positive solutions given by Jeanjean,Zhang and Zhong[J. Math. Pures Appl. (9) 183 (2024), 44–75], we give an alternative approach and extend the existence of infinitely many sign-changing normalized solutions to all .
{"title":"Infinitely many sign-changing normalized solutions for nonlinear scalar field equations","authors":"Jiaxin Zhan , Jianjun Zhang , Xuexiu Zhong , Jinfang Zhou","doi":"10.1016/j.aml.2024.109426","DOIUrl":"10.1016/j.aml.2024.109426","url":null,"abstract":"<div><div>We study the existence of infinitely many sign-changing solutions to the following nonlinear scalar Schrödinger equation <span><span><span><math><mrow><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>λ</mi><mi>u</mi><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mspace></mspace><mtext>in</mtext><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></math></span></span></span>with a prescribed mass <span><math><mrow><msub><mrow><mo>∫</mo></mrow><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></msub><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mi>d</mi><mi>x</mi><mo>=</mo><mi>a</mi><mo>.</mo></mrow></math></span> Here <span><math><mrow><mi>f</mi><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>R</mi><mo>,</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><mi>a</mi><mo>></mo><mn>0</mn></mrow></math></span> is a given constant and <span><math><mrow><mi>λ</mi><mo>∈</mo><mi>R</mi></mrow></math></span> is an unknown parameter appearing as a Lagrange multiplier. Jeanjean and Lu have established the existence of infinitely many sign-changing normalized solutions in [Nonlinearity 32 (2019), no. 12, 4942–4966] and [Calc. Var. Partial Differential Equations 59 (2020), no. 5, Paper No. 174, 43 pp.] for <span><math><mrow><mi>N</mi><mo>=</mo><mn>4</mn></mrow></math></span> or <span><math><mrow><mi>N</mi><mo>≥</mo><mn>6</mn></mrow></math></span>. After fully utilizing the properties of positive solutions given by Jeanjean,Zhang and Zhong[J. Math. Pures Appl. (9) 183 (2024), 44–75], we give an alternative approach and extend the existence of infinitely many sign-changing normalized solutions to all <span><math><mrow><mi>N</mi><mo>≥</mo><mn>2</mn></mrow></math></span>.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109426"},"PeriodicalIF":2.9,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874400","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 : 2024-12-14DOI: 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":"10.1016/j.aml.2024.109424","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109424"},"PeriodicalIF":2.9,"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 : 2024-12-12DOI: 10.1016/j.aml.2024.109425
Shuyu Li , Hong Wang , Jinhong Jia
We investigate a local modification of a variable-order time-fractional wave equation, which models the vibrations of a viscoelastic bar along its longitudinal axis. Under suitable assumptions regarding the variable order at , we prove that the original model is equivalent to a multiscale wave equation. Furthermore, we analyze the well-posedness of its weak solution. Numerical experiments are implemented to clarify the theoretical analysis.
{"title":"Local modification and analysis of a variable-order fractional wave equation","authors":"Shuyu Li , Hong Wang , Jinhong Jia","doi":"10.1016/j.aml.2024.109425","DOIUrl":"10.1016/j.aml.2024.109425","url":null,"abstract":"<div><div>We investigate a local modification of a variable-order time-fractional wave equation, which models the vibrations of a viscoelastic bar along its longitudinal axis. Under suitable assumptions regarding the variable order at <span><math><mrow><mi>t</mi><mo>=</mo><mn>0</mn></mrow></math></span>, we prove that the original model is equivalent to a multiscale wave equation. Furthermore, we analyze the well-posedness of its weak solution. Numerical experiments are implemented to clarify the theoretical analysis.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109425"},"PeriodicalIF":2.9,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874419","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 in a bounded domain. We allow both the nonlinear terms and 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 -estimates and dissipative -estimates for the solutions and further enhance the regularity results.
{"title":"Global L∞-estimates and dissipative H2-estimates of solutions for retarded reaction–diffusion equations","authors":"Ruijing Wang , Chunqiu Li","doi":"10.1016/j.aml.2024.109423","DOIUrl":"10.1016/j.aml.2024.109423","url":null,"abstract":"<div><div>This paper is concerned with the retarded reaction–diffusion equation <span><math><mrow><msub><mrow><mi>∂</mi></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>+</mo><mi>G</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow><mo>+</mo><mi>h</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> in a bounded domain. We allow both the nonlinear terms <span><math><mi>f</mi></math></span> and <span><math><mi>G</mi></math></span> 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 <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span>-estimates and dissipative <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-estimates for the solutions and further enhance the regularity results.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109423"},"PeriodicalIF":2.9,"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":"10.1016/j.aml.2024.109422","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109422"},"PeriodicalIF":2.9,"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":"10.1016/j.aml.2024.109414","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109414"},"PeriodicalIF":2.9,"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":"OA","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 -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 (2+1)-dimensional generalized Kadomtsev–Petviashvili equation","authors":"Zhenjie Niu, Biao Li","doi":"10.1016/j.aml.2024.109411","DOIUrl":"10.1016/j.aml.2024.109411","url":null,"abstract":"<div><div>The primary purpose of this work is to consider a <span><math><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional generalized KP equation via <span><math><mover><mrow><mi>∂</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span>-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 <span><math><mover><mrow><mi>∂</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span> derivative, a <span><math><mover><mrow><mi>∂</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span> problem arises naturally. Based on the symmetry of the Green function, we give a standard <span><math><mover><mrow><mi>∂</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span> equation, and its solution is expressed by the Cauchy formula.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109411"},"PeriodicalIF":2.9,"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 where , and appears as a Lagrange multiplier. When 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":"10.1016/j.aml.2024.109415","url":null,"abstract":"<div><div>We are interested in the following problem <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><msup><mrow><mi>Δ</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><mi>λ</mi><mi>u</mi><mo>=</mo><mi>g</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mtext>in</mtext><mspace></mspace><mspace></mspace><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mo>∫</mo></mrow><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></msub><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mi>d</mi><mi>x</mi><mo>=</mo><mi>c</mi><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>where <span><math><mrow><mi>N</mi><mo>≥</mo><mn>5</mn></mrow></math></span>, <span><math><mrow><mi>c</mi><mo>></mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>λ</mi><mo>∈</mo><mi>R</mi></mrow></math></span> appears as a Lagrange multiplier. When <span><math><mrow><mi>g</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow></mrow></math></span> 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.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109415"},"PeriodicalIF":2.9,"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":"10.1016/j.aml.2024.109412","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109412"},"PeriodicalIF":2.9,"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":"10.1016/j.aml.2024.109413","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109413"},"PeriodicalIF":2.9,"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}
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