Pub Date : 2025-10-09DOI: 10.1016/j.aml.2025.109782
Ying Chao , Jinqiao Duan , Pingyuan Wei
We investigate the exit problem from the domain of attraction of a stable state in kinetic Langevin systems with nongradient perturbations. Using Freidlin–Wentzell large deviation theory, we analyze the most probable escape paths and, through a Hamiltonian formulation combined with Melnikov theory, establish conditions under which the optimal escape path persists as a heteroclinic orbit in the perturbed system. Our results demonstrate that, in the presence of nongradient perturbations, the most probable escape path differs from the time-reversed heteroclinic orbit at leading order in the intensity of the autonomous perturbation. These theoretical findings are corroborated by a numerical example.
{"title":"Most probable escape paths in perturbed kinetic Langevin systems","authors":"Ying Chao , Jinqiao Duan , Pingyuan Wei","doi":"10.1016/j.aml.2025.109782","DOIUrl":"10.1016/j.aml.2025.109782","url":null,"abstract":"<div><div>We investigate the exit problem from the domain of attraction of a stable state in kinetic Langevin systems with nongradient perturbations. Using Freidlin–Wentzell large deviation theory, we analyze the most probable escape paths and, through a Hamiltonian formulation combined with Melnikov theory, establish conditions under which the optimal escape path persists as a heteroclinic orbit in the perturbed system. Our results demonstrate that, in the presence of nongradient perturbations, the most probable escape path differs from the time-reversed heteroclinic orbit at leading order in the intensity of the autonomous perturbation. These theoretical findings are corroborated by a numerical example.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109782"},"PeriodicalIF":2.8,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145268035","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 : 2025-10-08DOI: 10.1016/j.aml.2025.109783
Yuanyuan Xu, Shuyang Xue
In this paper, we investigate the spatiotemporal dynamics in the nonlocal advection–diffusion equation with delay. The nonlocal advection is characterized by the top-hat kernel and time delay measures the delay phenomenon in the reaction term. The joint effect of the nonlocal advection and delay on the stability of the steady state and spatiotemporal dynamics is investigated. The conditions for the occurrence of Turing bifurcation and Turing–Hopf bifurcation are determined. Our results show that the large perception range can stabilize the steady state, but a small perception range is more likely to make the system unstable, and negative feedback of delay is more easy to make system produce complex patterns. It has also been shown that spatially inhomogeneous oscillatory patterns are triggered by the joint interaction of nonlocal advection and delay, which can not occur only for one factor.
{"title":"Spatiotemporal patterns driven by the nonlocal advection and delay","authors":"Yuanyuan Xu, Shuyang Xue","doi":"10.1016/j.aml.2025.109783","DOIUrl":"10.1016/j.aml.2025.109783","url":null,"abstract":"<div><div>In this paper, we investigate the spatiotemporal dynamics in the nonlocal advection–diffusion equation with delay. The nonlocal advection is characterized by the top-hat kernel and time delay measures the delay phenomenon in the reaction term. The joint effect of the nonlocal advection and delay on the stability of the steady state and spatiotemporal dynamics is investigated. The conditions for the occurrence of Turing bifurcation and Turing–Hopf bifurcation are determined. Our results show that the large perception range can stabilize the steady state, but a small perception range is more likely to make the system unstable, and negative feedback of delay is more easy to make system produce complex patterns. It has also been shown that spatially inhomogeneous oscillatory patterns are triggered by the joint interaction of nonlocal advection and delay, which can not occur only for one factor.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109783"},"PeriodicalIF":2.8,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145267359","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 : 2025-10-05DOI: 10.1016/j.aml.2025.109781
Lin Liu , Baoting Su , Hongqing Song , Libo Feng
As a mathematical tool for addressing problems in unbounded domains, the absorbing boundary conditions derived by artificial boundary method are widely used in various scientific fields. This study mainly investigates the hydrodynamic behavior of Walter’s-B fluid over an inclined plate. Considering the effects of chemical reactions as well as the heat absorption/generation, the governing model is derived. By employing the -transform, the governing Eqs. defined in an unbounded domain are transformed into a computationally tractable finite domain, for which the finite difference method is applied. Numerical simulations are conducted to analyze the influence of various dimensionless parameters. Finally, a quantitative physical analysis is performed to evaluate the impact of these parameters on the concentration profile, temperature distribution, and velocity field.
{"title":"Numerical simulation of heat transfer and flow characteristics of Walter’s-B fluid over an inclined plate in a semi-infinite magnetic field","authors":"Lin Liu , Baoting Su , Hongqing Song , Libo Feng","doi":"10.1016/j.aml.2025.109781","DOIUrl":"10.1016/j.aml.2025.109781","url":null,"abstract":"<div><div>As a mathematical tool for addressing problems in unbounded domains, the absorbing boundary conditions derived by artificial boundary method are widely used in various scientific fields. This study mainly investigates the hydrodynamic behavior of Walter’s-B fluid over an inclined plate. Considering the effects of chemical reactions as well as the heat absorption/generation, the governing model is derived. By employing the <span><math><mi>z</mi></math></span>-transform, the governing Eqs. defined in an unbounded domain are transformed into a computationally tractable finite domain, for which the finite difference method is applied. Numerical simulations are conducted to analyze the influence of various dimensionless parameters. Finally, a quantitative physical analysis is performed to evaluate the impact of these parameters on the concentration profile, temperature distribution, and velocity field.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109781"},"PeriodicalIF":2.8,"publicationDate":"2025-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145320418","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 : 2025-10-04DOI: 10.1016/j.aml.2025.109784
Patrick Buchfink , Silke Glas , Hans Zwart
We combine energy-stable and port-Hamiltonian (pH) systems to obtain energy-stable port-Hamiltonian (es-pH) systems. The idea is to extend the known energy-stable systems with an input–output port, which results in a pH formulation. One advantage of the new es-pH formulation is that it naturally preserves its es-pH structure throughout discretization (in space and time) and model reduction.
{"title":"Energy-stable port-Hamiltonian systems","authors":"Patrick Buchfink , Silke Glas , Hans Zwart","doi":"10.1016/j.aml.2025.109784","DOIUrl":"10.1016/j.aml.2025.109784","url":null,"abstract":"<div><div>We combine energy-stable and port-Hamiltonian (<span>pH</span>) systems to obtain <em>energy-stable port-Hamiltonian (<span>es-pH</span>) systems</em>. The idea is to extend the known energy-stable systems with an input–output port, which results in a <span>pH</span> formulation. One advantage of the new <span>es-pH</span> formulation is that it naturally preserves its <span>es-pH</span> structure throughout discretization (in space and time) and model reduction.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109784"},"PeriodicalIF":2.8,"publicationDate":"2025-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145267360","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 : 2025-10-03DOI: 10.1016/j.aml.2025.109779
Anji Yang , Tingting Yu , Tonghua Zhang
Abrupt transitions between oligotrophic and eutrophic states have been observed in shallow lakes, yet the mechanisms underlying these transitions remain poorly understood. To investigate the evolution of a lake from an oligotrophic state to a eutrophic state and to determine the tipping time associated with this transition, we propose a probabilistic framework that characterizes the maximum likelihood transition path between the two states. We derive analytical expressions and numerical methods to calculate the maximum likelihood trajectories. Subsequently, we utilize the maximal likelihood trajectory to ascertain tipping times for the most probable transitions from oligotrophic to eutrophic states. Our findings indicate that increasing environmental stochasticity is associated with reduced tipping times, thereby promoting the eutrophication of lakes. Furthermore, tipping time serves as an effective metric for assessing the stability of the oligotrophic state; we posit that a shorter tipping time correlates with greater instability within the oligotrophic state.
{"title":"Tipping time in a stochastic phosphorus dynamics model","authors":"Anji Yang , Tingting Yu , Tonghua Zhang","doi":"10.1016/j.aml.2025.109779","DOIUrl":"10.1016/j.aml.2025.109779","url":null,"abstract":"<div><div>Abrupt transitions between oligotrophic and eutrophic states have been observed in shallow lakes, yet the mechanisms underlying these transitions remain poorly understood. To investigate the evolution of a lake from an oligotrophic state to a eutrophic state and to determine the tipping time associated with this transition, we propose a probabilistic framework that characterizes the maximum likelihood transition path between the two states. We derive analytical expressions and numerical methods to calculate the maximum likelihood trajectories. Subsequently, we utilize the maximal likelihood trajectory to ascertain tipping times for the most probable transitions from oligotrophic to eutrophic states. Our findings indicate that increasing environmental stochasticity is associated with reduced tipping times, thereby promoting the eutrophication of lakes. Furthermore, tipping time serves as an effective metric for assessing the stability of the oligotrophic state; we posit that a shorter tipping time correlates with greater instability within the oligotrophic state.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109779"},"PeriodicalIF":2.8,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145229518","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 : 2025-10-01DOI: 10.1016/j.aml.2025.109780
Yawen Mao , Chen Xu , Jiahe Yu , Feng Ding
This letter proposes a multiple-direction conjugate gradient (MD-CG) iterative algorithm accelerated by Gram–Schmidt -orthogonalization for parameter estimation in nonlinear NARMAX systems. Unlike the traditional CG algorithm that updates along a single conjugate direction per iteration, the MD-CG algorithm generates mutually -orthogonal search directions through a modified Gram–Schmidt process, and the convergence speed increases with increasing . Theoretical analysis shows that the convergence speed of the MD-CG algorithm can reach th power acceleration of the CG algorithm under ideal conditions, and is especially suitable for large-scale systems. A simulation example is provided to verify the superiority of the proposed algorithm in terms of parameter estimation speed and accuracy.
本文提出了一种由Gram-Schmidt a -正交化加速的多方向共轭梯度（MD-CG）迭代算法，用于非线性NARMAX系统的参数估计。与传统CG算法每次迭代沿单一共轭方向更新不同，MD-CG算法通过改进的Gram-Schmidt过程生成p个相互a正交的搜索方向，并且收敛速度随着p的增加而增加。理论分析表明，MD-CG算法的收敛速度在理想条件下可以达到CG算法的p次幂加速度，特别适用于大型系统。仿真实例验证了该算法在参数估计速度和精度方面的优越性。
{"title":"Multiple-direction conjugate gradient method via Gram–Schmidt A-orthogonalization with applications to nonlinear system identification","authors":"Yawen Mao , Chen Xu , Jiahe Yu , Feng Ding","doi":"10.1016/j.aml.2025.109780","DOIUrl":"10.1016/j.aml.2025.109780","url":null,"abstract":"<div><div>This letter proposes a multiple-direction conjugate gradient (MD-CG) iterative algorithm accelerated by Gram–Schmidt <span><math><mi>A</mi></math></span>-orthogonalization for parameter estimation in nonlinear NARMAX systems. Unlike the traditional CG algorithm that updates along a single conjugate direction per iteration, the MD-CG algorithm generates <span><math><mi>p</mi></math></span> mutually <span><math><mi>A</mi></math></span>-orthogonal search directions through a modified Gram–Schmidt process, and the convergence speed increases with increasing <span><math><mi>p</mi></math></span>. Theoretical analysis shows that the convergence speed of the MD-CG algorithm can reach <span><math><mi>p</mi></math></span>th power acceleration of the CG algorithm under ideal conditions, and is especially suitable for large-scale systems. A simulation example is provided to verify the superiority of the proposed algorithm in terms of parameter estimation speed and accuracy.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109780"},"PeriodicalIF":2.8,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145268033","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 : 2025-09-30DOI: 10.1016/j.aml.2025.109776
Di Lei, Huiyan Li, Jing Niu
This paper focuses on proving the stability of the Runge–Kutta spectral volume (RKSV) scheme for solving one-dimensional equations, with a specific analysis of the Radau spectral volume (RRSV) and Gauss–Legendre spectral volume (LSV) schemes. By comparing the similarities and discrepancies between the Runge–Kutta spectral volume (RKSV) and Runge–Kutta discontinuous Galerkin (RKDG) schemes, we transform the stability analysis of the RKSV scheme into that of the RKDG scheme-an approach that already possesses a well-established theoretical analysis basis. Our key findings reveal two critical results: first, the Runge–Kutta Radau spectral volume (RKRRSV) scheme is entirely equivalent to the RKDG scheme; second, under the framework of a newly defined norm, the Runge–Kutta Gauss–Legendre spectral volume (RKLSV) scheme yields stability results identical to those of the RKDG scheme. Furthermore, numerical experiments are conducted to validate both the stability and optimal convergence properties of the RKSV scheme, providing empirical support for its theoretical conclusions.
{"title":"The stability of Runge–Kutta spectral volume methods for 1-D linear hyperbolic equations with constant coefficients","authors":"Di Lei, Huiyan Li, Jing Niu","doi":"10.1016/j.aml.2025.109776","DOIUrl":"10.1016/j.aml.2025.109776","url":null,"abstract":"<div><div>This paper focuses on proving the stability of the Runge–Kutta spectral volume (RKSV) scheme for solving one-dimensional equations, with a specific analysis of the Radau spectral volume (RRSV) and Gauss–Legendre spectral volume (LSV) schemes. By comparing the similarities and discrepancies between the Runge–Kutta spectral volume (RKSV) and Runge–Kutta discontinuous Galerkin (RKDG) schemes, we transform the stability analysis of the RKSV scheme into that of the RKDG scheme-an approach that already possesses a well-established theoretical analysis basis. Our key findings reveal two critical results: first, the Runge–Kutta Radau spectral volume (RKRRSV) scheme is entirely equivalent to the RKDG scheme; second, under the framework of a newly defined norm, the Runge–Kutta Gauss–Legendre spectral volume (RKLSV) scheme yields stability results identical to those of the RKDG scheme. Furthermore, numerical experiments are conducted to validate both the stability and optimal convergence properties of the RKSV scheme, providing empirical support for its theoretical conclusions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109776"},"PeriodicalIF":2.8,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220890","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 : 2025-09-30DOI: 10.1016/j.aml.2025.109777
Xi-Hu Wu , Run-Fa Zhang
Spin waves, as charge-free collective excitations of electron spins, are fundamental to the development of energy-efficient spintronic devices and wave-based computing. This Letter investigates a higher-order Heisenberg ferromagnetic model characterizing the dynamics of the magnetic vector in isotropic ferromagnetism. We construct a direct -fold Darboux transformation (DT) and a generalized -fold DT in the compact determinant forms, which enhance the efficiency of obtaining rogue wave, multiple, multi-pole and mixed solutions for the nonlinear systems within the Heisenberg ferromagnetic hierarchy. Those results also help provide a mathematical framework for exploring complex spin wave interactions in ferromagnetic materials.
{"title":"Compact Darboux transformation and multi-pole magnetic waves within a higher-order Heisenberg ferromagnetic model","authors":"Xi-Hu Wu , Run-Fa Zhang","doi":"10.1016/j.aml.2025.109777","DOIUrl":"10.1016/j.aml.2025.109777","url":null,"abstract":"<div><div>Spin waves, as charge-free collective excitations of electron spins, are fundamental to the development of energy-efficient spintronic devices and wave-based computing. This Letter investigates a higher-order Heisenberg ferromagnetic model characterizing the dynamics of the magnetic vector in isotropic ferromagnetism. We construct a direct <span><math><mi>N</mi></math></span>-fold Darboux transformation (DT) and a generalized <span><math><mi>N</mi></math></span>-fold DT in the compact determinant forms, which enhance the efficiency of obtaining rogue wave, multiple, multi-pole and mixed solutions for the nonlinear systems within the Heisenberg ferromagnetic hierarchy. Those results also help provide a mathematical framework for exploring complex spin wave interactions in ferromagnetic materials.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109777"},"PeriodicalIF":2.8,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220889","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 : 2025-09-30DOI: 10.1016/j.aml.2025.109775
Xin Zhang , Lin Li , Jijiang Sun
In this paper, we study the following degenerate Kirchhoff-type problem where is a bounded smooth domain, are constants, and . Using genus theory, symmetric mountain pass lemma and cut-off technique, we prove the existence of infinitely many solutions for an odd nonlinearity . Depending on whether is superlinear or sublinear at the origin, we show that the corresponding solution sequence either has energies concentrating at the critical level or converges to zero in the norm.
{"title":"Multiplicity and asymptotic behavior of solutions for a degenerate Kirchhoff type problem","authors":"Xin Zhang , Lin Li , Jijiang Sun","doi":"10.1016/j.aml.2025.109775","DOIUrl":"10.1016/j.aml.2025.109775","url":null,"abstract":"<div><div>In this paper, we study the following degenerate Kirchhoff-type problem <span><span><span><math><mfenced><mrow><mtable><mtr><mtd></mtd><mtd><mo>−</mo><mfenced><mrow><mi>a</mi><mo>−</mo><mi>b</mi><msub><mrow><mo>∫</mo></mrow><mrow><mi>Ω</mi></mrow></msub><msup><mrow><mrow><mo>|</mo><mo>∇</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mi>d</mi><mi>x</mi></mrow></mfenced><mi>Δ</mi><mi>u</mi><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>)</mo></mrow><mo>,</mo><mspace></mspace><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd></mtd><mtd><mi>u</mi><mo>=</mo><mn>0</mn><mo>,</mo><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mi>x</mi><mo>∈</mo><mi>∂</mi><mi>Ω</mi><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>where <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mrow><mo>(</mo><mi>N</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></mrow></mrow></math></span> is a bounded smooth domain, <span><math><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>></mo><mn>0</mn></mrow></math></span> are constants, and <span><math><mrow><mi>f</mi><mo>∈</mo><mi>C</mi><mrow><mo>(</mo><mi>Ω</mi><mo>×</mo><mi>R</mi><mo>,</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span>. Using genus theory, symmetric mountain pass lemma and cut-off technique, we prove the existence of infinitely many solutions for an odd nonlinearity <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>)</mo></mrow></mrow></math></span>. Depending on whether <span><math><mi>f</mi></math></span> is superlinear or sublinear at the origin, we show that the corresponding solution sequence either has energies concentrating at the critical level <span><math><mrow><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>/</mo><mrow><mo>(</mo><mn>4</mn><mi>b</mi><mo>)</mo></mrow></mrow></math></span> or converges to zero in the <span><math><msubsup><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn></mrow></msubsup></math></span> norm.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109775"},"PeriodicalIF":2.8,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145268034","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 : 2025-09-30DOI: 10.1016/j.aml.2025.109778
Rui Wang , Juntao Sun , Sofiane Khoutir , Han-Su Zhang
In this paper, we are concerned with the multiplicity of normalized solutions for a class of Kirchhoff equations with the nonlinearity in , where and . We explore the relationship between the number of solutions and the shape of the weight function .
{"title":"Multiple normalized solutions for non-autonomous Kirchhoff equations with mass-subcritical nonlinearity in R3","authors":"Rui Wang , Juntao Sun , Sofiane Khoutir , Han-Su Zhang","doi":"10.1016/j.aml.2025.109778","DOIUrl":"10.1016/j.aml.2025.109778","url":null,"abstract":"<div><div>In this paper, we are concerned with the multiplicity of normalized solutions for a class of Kirchhoff equations with the nonlinearity <span><math><mrow><mi>h</mi><mrow><mo>(</mo><mi>ɛ</mi><mi>x</mi><mo>)</mo></mrow><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi></mrow></math></span> in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>, where <span><math><mrow><mi>ɛ</mi><mo>></mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mn>4</mn><mo>≤</mo><mi>p</mi><mo><</mo><mn>14</mn><mo>/</mo><mn>3</mn></mrow></math></span>. We explore the relationship between the number of solutions and the shape of the weight function <span><math><mi>h</mi></math></span>.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"173 ","pages":"Article 109778"},"PeriodicalIF":2.8,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220885","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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