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26 February 2025, Volume 45 Issue 1 Previous Issue    Next Issue

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Normalized Solutions of the Quasilinear Schrödinger System in Bounded Domains Zhang Qian Acta mathematica scientia,Series A. 2025, 45 (1):  1-30.  Abstract ( 300 )   RICH HTML PDF (779KB) ( 418 )   Save This paper is concerned with the following nonlinear coupled system $\left\{\begin{array}{l} -\Delta u_{1}+\omega_{1} u_{1}-\frac{1}{2} \Delta\left(u_{1}^{2}\right) u_{1}=\mu_{1}\left|u_{1}\right|^{p-1} u_{1}+\beta\left|u_{2}\right|^{\frac{p+1}{2}}\left|u_{1}\right|^{\frac{p-3}{2}} u_{1} \\ -\Delta u_{2}+\omega_{2} u_{2}-\frac{1}{2} \Delta\left(u_{2}^{2}\right) u_{2}=\mu_{2}\left|u_{2}\right|^{p-1} u_{2}+\beta\left|u_{1}\right|^{\frac{p+1}{2}}\left|u_{2}\right|^{\frac{p-3}{2}} u_{2} \\ \int_{\Omega}\left|u_{i}\right|^{2} \mathrm{~d} x=\rho_{i}, \quad i=1,2, \quad\left(u_{1}, u_{2}\right) \in H_{0}^{1}\left(\Omega ; \mathbb{R}^{2}\right) \end{array}\right.$ and linear coupled system $\left\{\begin{array}{l} -\Delta u_{1}+\omega_{1} u_{1}-\frac{1}{2} \Delta\left(u_{1}^{2}\right) u_{1}=\mu_{1}\left|u_{1}\right|^{p-1} u_{1}+\beta u_{2} \\ -\Delta u_{2}+\omega_{2} u_{2}-\frac{1}{2} \Delta\left(u_{2}^{2}\right) u_{2}=\mu_{2}\left|u_{2}\right|^{p-1} u_{2}+\beta u_{1} \\ \int_{\Omega}\left|u_{i}\right|^{2} \mathrm{~d} x=\rho_{i}, \quad i=1,2, \quad\left(u_{1}, u_{2}\right) \in H_{0}^{1}\left(\Omega ; \mathbb{R}^{2}\right) \end{array}\right.$ where $\Omega\subset\mathbb R^N(N\geq1)$ is a bounded smooth domain, $\omega_i,\ \beta\in\mathbb R$, $\mu_i,\ \rho_i>0,\ i=1,2.$ Moreover, $p>1$ if $N=1,2$ and $1<p\leqslant\frac{3N+2}{N-2}$ if $N\geqslant3$. Using change of variables, on the one hand, we prove the existence and stability of normalized solutions in nonlinear coupled system and the limiting behavior of normalized solutions as $\beta\rightarrow -\infty$. On the other hand, we apply the minimization constraint technique to obtain the existence of normalized solutions for linear coupled system. Compared with some previous results, we extend the existing results to the quasilinear Schrödinger system and also obtain normalized solutions for the linear coupling case. References | Related Articles | Metrics

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Existence and Uniqueness of Solutions for Sub-Linear Heat Equations with Almost Periodic Coefficients Ren Chenchen, Yang Sudan Acta mathematica scientia,Series A. 2025, 45 (1):  31-43.  Abstract ( 146 )   RICH HTML PDF (558KB) ( 207 )   Save In nature, almost periodic functions are "much more" than periodic functions, and an influential generalization of almost periodic functions is the asymptotic almost periodic function proposed by the famous mathematician M Fréchet in the study of almost periodic motions with perturbations. Thanks to this perturbative term, asymptotically almost periodic functions have a wider range of applications. In this paper, we study the existence and uniqueness of asymptotically almost periodic solutions of sub-linear heat equations with asymptotically almost periodic coefficients. References | Related Articles | Metrics

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Asymptotic Stability of Pyramidal Traveling Front for Nonlocal Delayed Diffusion Equation Liu Jia, Bao Xiongxiong Acta mathematica scientia,Series A. 2025, 45 (1):  44-53.  Abstract ( 106 )   RICH HTML PDF (625KB) ( 198 )   Save The nonplanar traveling fronts of reaction-diffusion equations have been attracted a lot of attention and pyramidal traveling fronts for the nonlocal delayed diffusion equation are also established in $\Bbb{R}^{N}$ with $N\geq 3$. In fact, the uniqueness and stability for such $N$-dimensional pyramidal traveling fronts are very interesting problems. The current paper shows that the pyramidal traveling front for the nonlocal delayed diffusion equation in $\Bbb{R}^{3}$ is uniquely determined, which is asymptotically stable when the initial perturbations decay at infinity. References | Related Articles | Metrics

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A Universal Inequality for the Dirichlet Eigenvalue Problem of the Weighted Laplacian and its Application Yang Guicheng, Wen Yangzhe, Mao Jing Acta mathematica scientia,Series A. 2025, 45 (1):  54-73.  Abstract ( 106 )   RICH HTML PDF (629KB) ( 141 )   Save In this paper, we study the Dirichlet eigenvalue problem of the weighted Laplace operator $\mathbb {L}_\phi$ on a bounded domain $\Omega$ with a smooth boundary in $n$-dimensional Euclidean space. Under the premise that the weighted function $\phi$ satisfies certain constraints, a universal inequality of the eigenvalue problem can be obtained by using the variational method and constructing the test function appropriately. References | Related Articles | Metrics

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The Asymptotic Behavior of the Generalized Brinkman-Forchheimer Equation Li Xin, Hao Wenjuan, Liu Yang Acta mathematica scientia,Series A. 2025, 45 (1):  74-91.  Abstract ( 98 )   RICH HTML PDF (656KB) ( 191 )   Save This article investigated the well-posedness and long-term behavior problems of solutions to 3D compressible generalized Brinkman-Forchheimer equation defined on a bounded domain. The equation simulates the transport process of fluid through porous medium dominated by Lévy dissipation. Firstly, the classical compactness method and a prior estimation were used to prove the well posedness of the solution of the equation in the energy space. Secondly, introduce the concept of system decomposition: on the one hand, the localization method was used to prove the boundedness of the contraction part of the equation in the initial energy space; on the other hand, the exponential dissipation of the smooth part of the equation in the high-order energy space is obtained by the instantaneous optical smoothing method, and the existence of the global attractor and the exponential attractor of the equation in the initial phase space is finally verified. References | Related Articles | Metrics

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Existence of Multiple Solutions for a Fractional $p$-Kirchhoff Equation Pan Rou, Chen Lin Acta mathematica scientia,Series A. 2025, 45 (1):  92-100.  Abstract ( 66 )   RICH HTML PDF (529KB) ( 107 )   Save In this paper, by constructing the Nehari manifold and defining the corresponding fibering map, we discuss the existence of multiple solutions for a class of fractional $p$-Kirchhoff equation. References | Related Articles | Metrics

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Continuous Dependence of Harmonic Equations on Base Perturbation in Prismatic Cylinder Chen Xuejiao, Li Dandan, Shi Jincheng, Zeng Peng Acta mathematica scientia,Series A. 2025, 45 (1):  101-109.  Abstract ( 60 )   RICH HTML PDF (530KB) ( 92 )   Save This article establishes the continuous dependence of the harmonic equation on its basic geometry and load of the decay behaviour in a prismatic semi-infinite cylinder. Assuming that the harmonic equation on the side of the cylinder satisfies homogeneous boundary conditions, a differential inequality technique is used to derive a differential inequality for perturbation of geometric bases and differences in solutions. This differential inequality can directly derive the continuous dependence of the solution on perturbation parameters and known data on the base. References | Related Articles | Metrics

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Traveling Wave Solutions to a Cholera Epidemic System with Spatio-Temporal Delay and Nonlocal Dispersal Yang Yongli, Yang Yunrui Acta mathematica scientia,Series A. 2025, 45 (1):  110-135.  Abstract ( 67 )   RICH HTML PDF (699KB) ( 239 )   Save This paper deals with the existence, non-existence and asymptotic behaviors of traveling wave solutions to a class of cholera epidemic system with spatio-temporal delay and nonlocal dispersal. By constructing the upper and lower solutions, the existence of traveling waves to the system is converted into the fixed point problem of a nonlinear operator on a closed and convex cone, and thus the existence, boundedness and asymptotic behavior at negative infinity of traveling waves of the system are proved by applying Schauder's fixed point theorem, limit theory and analysis techniques. In addition, the nonexistence of traveling waves of the system is also established based on the two-sided Laplace transform and the method of proof by contradiction. References | Related Articles | Metrics

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Reduction and Summation Formulas for Two Types of Kampé de Fériet Series Liu Hongmei, Li Yang Acta mathematica scientia,Series A. 2025, 45 (1):  136-152.  Abstract ( 42 )   RICH HTML PDF (546KB) ( 186 )   Save Two $_3F_2[1]$-summation theorems are employed to establish two general transformation formulas for double infinite series. With the help of some classical hypergeometric series summation formulas, the two transformations yield a number of summation formulas for Kampé de Fériet series of type $F_{q:1;0}^{p:2;1}$. Furthermore a list of reduction and transformation formulas for Kampé de Fériet series of type $F_{q:1;1}^{p:2;2}$ are derived by utilizing four Saalschützian $_4F_3[1]$-summation formulas. References | Related Articles | Metrics

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Combining RKM with FDM for Time Fractional Convection-Diffusion Equations with Variable Coefficients Lv Xueqin, He Songyan, Wang Shiyu Acta mathematica scientia,Series A. 2025, 45 (1):  153-164.  Abstract ( 57 )   RICH HTML PDF (1356KB) ( 75 )   Save In this paper, we will study the time fractional convection-diffusion equation with variable coefficients. First, we use the finite difference method. The time variable is discretized, and the semi-discrete scheme of the equation is obtained. The exact solution $u(x,t_{n})$ of the equation is obtained by using the theory of reproducing kernel method. Then the exact solution $u(x,t_{n})$ is truncated by $m$ term to obtain the approximate solution $u_{m}(x,t_{n})$. By proving, we know that the method is stable. Moreover, $u_{m}^{(i)}(x,t_{n})$ converge uniformly to $u^{(i)}(x,t_{n})$ $(i=0,1,2)$. Finally, we give several numerical examples and compare them with the methods in other literatures, which show that our algorithm is effective. Figures and Tables | References | Related Articles | Metrics

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Nonmonotone Smoothing Inexact Newton Algorithm for Solving Weighted Horizontal Linear Complementarity Problems Fan Tiantian, Tang Jingyong, Zhou Jinchuan Acta mathematica scientia,Series A. 2025, 45 (1):  165-179.  Abstract ( 55 )   RICH HTML PDF (621KB) ( 209 )   Save In this paper, we study a nonmonotone smoothing inexact Newton algorithm for solving the weighted horizontal linear complementarity problem (wHLCP). The algorithm uses a smoothing function to reformulate the wHLCP as a nonlinear system of equations and then solve it by inexact Newton's method. Since inexact directions are not necessarily descent, the algorithm adopts a new nonmonotone line search technique to ensure its globalization. Especially, we prove that the generated iteration sequence is bounded under the ${P}$-pair condition. Moreover, we analyze the local convergence rate of the algorithm under the Hölderian local error bound condition which is more general than the local error bound condition. The algorithm solves the nonlinear equations only approximately so that a lot of computation time can be saved. Numerical experiment results confirm the advantage of the algorithm. Figures and Tables | References | Related Articles | Metrics

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Application of Cubic MQ Quasi-Interpolation in Derivative Approximations Under Random Perturbation Zhang Shengliang, Qian Yanyan Acta mathematica scientia,Series A. 2025, 45 (1):  180-188.  Abstract ( 53 )   RICH HTML PDF (965KB) ( 193 )   Save This paper proposes a numerical method that can effectively approximate high-order derivatives under random perturbation based on the cubic MQ (multiquadric) quasi-interpolation operator. Corresponding numerical examples and error estimates are given. Numerical experimental results show that the proposed method is more accurate, more stable and more effective than the existing methods. Figures and Tables | References | Related Articles | Metrics

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Integral Averages forms and Harmonic Beltrami Differentials Huo Shengjin, Shao Wanting Acta mathematica scientia,Series A. 2025, 45 (1):  189-202.  Abstract ( 51 )   RICH HTML PDF (633KB) ( 200 )   Save In this paper we investigate the relationship between the integral averages norms of some analytic functions and the harmonic Beltrami differentials induced by some holomorphic quadratic differentials. We discuss that under what conditions are the holomorphic forms with finite asymptotic variances. The paper offers a new criterion method for a harmonic Beltrami differential belonging to the Weil-Petersson class by the integral means norms. Furthermore we give a method of determining a homeomorphism $g$ of the unit circle $\partial\Delta$ belonging to Sobolev class $H^{\frac{3}{2}}$. References | Related Articles | Metrics

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Oscillation Analysis of Numerical Solutions for a Class of Nonlinear Delay Differential Equations with Variable Coefficients Hu Bingbing, Gao Jianfang Acta mathematica scientia,Series A. 2025, 45 (1):  203-213.  Abstract ( 56 )   RICH HTML PDF (530KB) ( 215 )   Save This article considers the oscillation of numerical solutions for a class of nonlinear delay differential equations with variable coefficients. By using the linear $\theta$-methods and linearization theory, the oscillation of the nonlinear difference equation is transformed into that of its corresponding linearized equation. By using inequality comparisons and scaling techniques, the conditions of the oscillation for the numerical solutions are obtained. Figures and Tables | References | Related Articles | Metrics

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Stability of Error Bounds for Multifunctions Shen Zongshan Acta mathematica scientia,Series A. 2025, 45 (1):  214-235.  Abstract ( 70 )   RICH HTML PDF (605KB) ( 151 )   Save In terms of the Slater condition of the Bouligand and Clarke tangent derivatives of the objective multifunction $\Psi$, this paper mainly studies the stability of error bound of $\Psi$ at a point $\bar{x}$ with respect to an ordering cone $C$. It is proved that the Slater condition of the Bouligand tangent derivative of $\Psi$ at $\bar{x}$ with respect to $C$ is always stable with respect to all small calm perturbations. Based on this result, we prove that the Slater condition of the Bouligand tangent derivative of $\Psi$ at $\bar{x}$ with respect to $C$ is a sufficient condition for $\Psi$ to have a stable error bound at $\bar{x}$ with respect to $C$ when $\Psi$ undergoes small calm and regular perturbations. These results extend the corresponding ones given by Zheng [Math Oper Res, 2022, 47(4): 3282--3303] from the vector-valued to the set-valued case. As applications, some sufficient conditions are provided for a convex progress to have a stable global error bound with respect to an ordering cone. References | Related Articles | Metrics

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A New Projection Algorithm for Solving Quasimonotone Variational Inequality Problems and Fixed Point Problems Wang Wujing, Zhu Meiling, Zhang Yongle Acta mathematica scientia,Series A. 2025, 45 (1):  236-255.  Abstract ( 57 )   RICH HTML PDF (734KB) ( 76 )   Save In this paper, we introduce a new inertial Tseng's extragradient algorithm for finding a common element of the set of solutions of a quasimonotone variational inequality problem and the set of fixed points of a demicontractive mapping in real Hilbert spaces. The strong convergence of the algorithm is proved under quasimonotone and uniformly continuous assumptions of the variational inequality mapping. Finally, some numerical examples illustrate the effectiveness of our algorithm. Figures and Tables | References | Related Articles | Metrics

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Iterative Algorithms of Common Elements for the Set of Solutions of Split Feasibility Problem and the Set of Common Fixed Points of a Finite Family of Quasi-Nonexpansive Operators Zhang Yuting, Gao Xinghui, Peng Jianying Acta mathematica scientia,Series A. 2025, 45 (1):  256-268.  Abstract ( 59 )   RICH HTML PDF (619KB) ( 72 )   Save In real Hilbert spaces, we construct a new algorithm to find a common solution of the split feasibility problem and the fixed points problem involving a finite family of quasi-nonexpansive mappings. Under appropriate conditions, it is proved that the iteration sequence by the algorithm strongly converges to a common solution of the split feasibility problem and the fixed points problem by using the demi-closed principle and properties of projection operators and conjugate operators. The effectiveness of the algorithm is verified by numerical experiments. The results of this paper improve and extend recent some relative results. Figures and Tables | References | Related Articles | Metrics

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Study on Parameter Identifiability of an Age-Structured Tuberculosis Model with Relapse Wu Ziyi, Yang Junyuan Acta mathematica scientia,Series A. 2025, 45 (1):  269-278.  Abstract ( 134 )   RICH HTML PDF (829KB) ( 239 )   Save The identifiability of model parameters plays a crucial role in determining the precision of model predictions. Additionally, predictions based on identifiable outcomes exhibit a higher degree of scientific rigor and accuracy. Unlike ordinary differential systems, achieving parameter identifiability in age-structured models with initial-boundary conditions poses considerable challenges. This paper aims to investigate the structural and practical identifiability of an age-structured tuberculosis model with relapse. First, we employ the eigenvalue method to ascertain the order of unidentifiable parameters. In conjunction with data provided by the Public Health Science Data Center, we employ Monte Carlo simulation to explore the practical identifiability of the proposed model. By calculating the Average Relative Error (ARE) for each parameter and utilizing the Fisher information matrix, we determine that all parameters are identifiable. Furthermore, we assess how uncertainty in these parameters affects tuberculosis transmission by analyzing the Fisher information matrix and partial rank correlation coefficient. Figures and Tables | References | Related Articles | Metrics

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Dynamical Analysis of an Age-Structured HIV Latent Model with Nonlocal Dispersal and Spatial Heterogeneity Wu Peng, Fang Cheng Acta mathematica scientia,Series A. 2025, 45 (1):  279-294.  Abstract ( 75 )   RICH HTML PDF (681KB) ( 217 )   Save The spatial heterogeneity and infection age profoundly affect the infection process of HIV in the within-host. In order to investigate the effects of spatial heterogeneity and infection age on the infection dynamics of HIV, in this paper, we propose an age structured and nonlocal diffusion HIV latent infection model to describe the diffusion of HIV in different organs of the within-host. Firstly, we investigate the global existence of the model solution. Secondly, by establishing the general update equation of the model, the next generation regeneration operator $\mathcal{R}$ is derived, and the basic regeneration number $R_0$ of the model is obtained as the spectral radius of the operator $\mathcal{R}$. As the dynamics threshold of the infectious disease model, $R_0$ determines the extinction and outbreak of HIV infection in the host. Finally, the existence of non trivial solutions for the system was proved by using Krasnoselskii fixed point theorem. In addition, the asymptotic profiles of the positive steady state of the system were proved in special case. References | Related Articles | Metrics

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Analysis of P2P Networks Based on Geo/G/1 Retrial Queue with Optional Vacation and Priority Ma Zhanyou, Qin Guoli, Jiang Zishu, Shen Ying Acta mathematica scientia,Series A. 2025, 45 (1):  295-304.  Abstract ( 70 )   RICH HTML PDF (686KB) ( 188 )   Save This article aims to construct a queuing model based on the dynamic changes in node states within a P2P network, enabling an accurate simulation of the dynamic trends of nodes within the system. Based on this model framework, a Geo/G/1 retrial queuing system was established with second optional vacation, priority, and impatient customers. To analyze the one-step state transition probabilities of each node within the network, the embedded Markov chain method was utilized and a Markov chain of the corresponding dimension was constructed. This paper used the supplementary variable method to derive the system of equilibrium equations satisfied by the system and obtained the performance indexes of various types of nodes within the network by solving the system of equations. The trend of the system's performance indexes with different parameters is also verified. Figures and Tables | References | Related Articles | Metrics