Table of Content

26 February 2018, Volume 38 Issue 1 Previous Issue    Next Issue

For Selected:

View Abstracts

Download Citations EndNote Reference Manager ProCite BibTeX RefWorks

Toggle Thumbnails

Select

Limit Cycles Bifurcating from a Class of Quasi-Homogeneous Polynomial Center Liang Haihua, Chen Yuming, Cen Xiuli Acta mathematica scientia,Series A. 2018, 38 (1):  1-9.  Abstract ( 161 )   RICH HTML PDF (414KB) ( 104 )   Save Determining the condition such that a planar quasi-homogeneous polynomial differential system has a center is a difficult topic. In this paper, we first extend the quintic quasi-homogeneous system, provided by[12], to the quasi-homogeneous polynomial system of degree n (odd number), and then give the necessary and sufficient condition to ensure that it possess a global center. Using the first order Melnikov function, we obtain the least upper bound for the number of limit cycles bifurcating from the period annulus of the center of the system, under the perturbation of polynomial of degree n. Finally, we prove that this conclusion is also true for the limit cycles bifurcating from all the (m,1)-(or (1,m)-) planar quasi-homogeneous polynomial differential Hamiltonian system, under polynomial perturbation of degree 2m-1, where m is any positive integer. References | Related Articles | Metrics

Select

Coefficient Estimate for Some Subclasses of Reciprocal Starlike Functions with Respect to Symmetric Conjugate Points Ma Lina, Li Shuhai, Niu Xiaomeng, Zhang Haiyan Acta mathematica scientia,Series A. 2018, 38 (1):  10-23.  Abstract ( 197 )   RICH HTML PDF (331KB) ( 121 )   Save In the present paper, we introduce some new classes of meromorphically reciprocal starlike functions with respect to symmetric conjugate points defined by subordination and obtain the integral representation and the coefficient estimates of the classes. The results improve the general known integral representations of meromorphic p-valent functions. Specially, we obtain the extreme function and give the graph of the range of the function. The results present here improve and generalize some known results. References | Related Articles | Metrics

Select

Multicomponent Perturbed AKNS Soliton Hierarchy Associated with the Lie Algebra sl(m + 1, R) Di Yanmei, Li Chunxia, Shen Shoufeng, Ma Wenxiu Acta mathematica scientia,Series A. 2018, 38 (1):  24-33.  Abstract ( 175 )   RICH HTML PDF (302KB) ( 231 )   Save A new multicomponent matrix spectral problem associated with the Lie algebra sl(m+1,R) is proposed, and new perturbed AKNS soliton hierarchy is generated by the corresponding zero curvature formulation. By virtue of the trace identity, a bi-Hamiltonian structure is established for the hierarchy, and a common hereditary recursion operator is explicitly worked out. References | Related Articles | Metrics

Select

Variable Homogeneous Besov and Triebel-Lizorkin Spaces on Stratified Groups Fang Jingxuan, Zhao Jiman Acta mathematica scientia,Series A. 2018, 38 (1):  34-45.  Abstract ( 129 )   RICH HTML PDF (369KB) ( 159 )   Save In this paper, we introduce the homogeneous Besov and Triebel-Lizorkin spaces with one variable exponent on Stratified groups. Then we show equivalent norms of these spaces. References | Related Articles | Metrics

Select

Two Inequalities Related to Generalized Elliptic Integrals Yin Li, Huang Liguo Acta mathematica scientia,Series A. 2018, 38 (1):  46-53.  Abstract ( 152 )   RICH HTML PDF (274KB) ( 126 )   Save In this paper, the authors mainly study monotonicity and convexity of the function Δp (r) where Kp and Ep denote the generalized elliptic integrals of the first and second kinds, respectively. Hence, we give two new inequalities. References | Related Articles | Metrics

Select

The Existence of Solutions for Choquard Type Equation Sun Xiaomei Acta mathematica scientia,Series A. 2018, 38 (1):  54-60.  Abstract ( 111 )   RICH HTML PDF (304KB) ( 77 )   Save In this paper, we consider the following Choquard type equation -Δpu+V(x)|u|p-2u=(|x|-(N-α) * F(u))f(u), where -Δpu=div(|▽ u|p-2▽ u) and x=(y,z)∈ RK×RN-K. Assume that the potential V(y,z) and the nonlinearity f satisfy suitable conditions, we prove the existence of solutions in the level of mountain pass for the above Choquard equation. References | Related Articles | Metrics

Select

Existence of Constrained Minimizers for Schrödinger-Poisson Equations in RN Zhu Xincai Acta mathematica scientia,Series A. 2018, 38 (1):  61-70.  Abstract ( 126 )   RICH HTML PDF (328KB) ( 101 )   Save In this paper, we concern with the existence of constrained minimizers for the variational problem (1.2). We give a classification of the exponent p determining the existence and nonexistence of minimizers. For any fixed a > 0, (1.2) admits minimizers if 0 < p < (4/N) and there is no minimizer of (1.2) if p > (4/N). Specially, if p=(4/N), the existence of minimizers is then proved if and only if a satisfies 0 < a ≤ a*:=||φ||2(4/N), where φ(x) is the unique (up to translations) positive radial solution of -Δ u(x)+u(x)=u1+(4/N)(x) in RN. Moreover, there is no minimizer of (1.2) if a > a*. References | Related Articles | Metrics

Select

Determining Modes and Determining Nodes to the Fluid Flow of Ladyzhenskaya Model Zhang Mingshu, Zhu Zheqi, Zhao Caidi Acta mathematica scientia,Series A. 2018, 38 (1):  71-82.  Abstract ( 163 )   RICH HTML PDF (376KB) ( 77 )   Save This article estimates the finite number of determining modes and determining nodes for the fluid flow of Ladyzhenskaya model on two-dimensional bounded smooth domains. The finite number of determining modes implies that the solutions of the addressed fluids are determined completely by their first finite number of Fourier modes. The determining nodes reveals that whenever two different solutions of the fluid have the same asymptotic behavior at finite number of points in the physical space, then they also possess the same asymptotic behavior at almost everywhere points of the physical space. References | Related Articles | Metrics

Select

The Inviscid and Non-Resistive Limit for 3D Nonhomogeneous Incompressible MHD Equations with a Slip Boundary Condition Chen Pengfei Acta mathematica scientia,Series A. 2018, 38 (1):  83-95.  Abstract ( 117 )   RICH HTML PDF (380KB) ( 95 )   Save In this paper, we investigate the inviscid and non-resistive limit of the 3D nonhomogeneous incompressible magnetohydrodynamic (MHD) equations in a class of bounded smooth domain with a slip boundary condition. We obtain the estimates on the rate of convergence in C([0,T],H2(Ω)). References | Related Articles | Metrics

Select

Long-Time Stability of Nonlinear Neutral Differential Equations with Variable Delay Wang Wansheng, Zhong Peng, Zhao Xinyang Acta mathematica scientia,Series A. 2018, 38 (1):  96-109.  Abstract ( 147 )   RICH HTML PDF (399KB) ( 93 )   Save The long-time behaviour of nonlinear neutral delay differential equations (NDDEs) with variable delay is analysed. A main result guaranteeing uniform ultimate boundedness for a variable delay nonlinear system has been established. The sufficient conditions for the uniform ultimate boundedness for two typical examples of NDDEs, the constant delay differential equations and the proportional delay differential equations, are derived from the main result. Some examples are given to illustrate the applications of these results. References | Related Articles | Metrics

Select

Global Existence and Exponential Decay of Solution for Some Higher-Order Wave Equation Ye Yaojun, Hu Yue Acta mathematica scientia,Series A. 2018, 38 (1):  110-121.  Abstract ( 141 )   RICH HTML PDF (347KB) ( 121 )   Save This paper deals with the initial-boundary value problem for a class of higher-order nonlinear wave equation with strong dissipative term in a bounded domain. We prove the existence of global solutions for this problem by constructing a stable set in H0m(Ω) and give the exponential decay estimate. Meanwhile, the blow-up result of solution in the unstable set is also obtained if the initial energy is positive. References | Related Articles | Metrics

Select

Uniform Decay for a Fourth-Order Viscoelastic Equation with Density in Rn Feng Baowei, Su Keqin Acta mathematica scientia,Series A. 2018, 38 (1):  122-133.  Abstract ( 129 )   RICH HTML PDF (365KB) ( 89 )   Save In this paper, we investigate a fourth-order linear viscoelastic equation with density in the whole space Rn (n ≥ 4). To compensate the lack of Poincaré's inequality in Rn, we consider the solutions in weighted spaces. Under suitable assumptions on the relaxation function, we establish a general decay result of solution for the initial value problem by using energy perturbation method. Our result extends earlier results. References | Related Articles | Metrics

Select

Oscillation for a Class of Second-Order Damped Emden-Fowler Dynamic Equations on Time Scales Yang Jiashan, Li Tongxing Acta mathematica scientia,Series A. 2018, 38 (1):  134-155.  Abstract ( 146 )   RICH HTML PDF (469KB) ( 82 )   Save The oscillation for certain second-order nonlinear neutral variable delay Emden-Fowler dynamic equations with damping on time scales is discussed. By using the time scales theory and the generalized Riccati transformation and the inequality technique, we establish six new oscillation criteria for the equations. Our results extend and improve some known results, but also unify the oscillation of second-order nonlinear damped Emden-Fowler differential equations and difference equations. Two examples are given to illustrate the main results of this article. References | Related Articles | Metrics

Select

The Asymptotic Behavior of the Solution in Structured Bacterial Population Model Wang Shenghua, Cheng Guofei Acta mathematica scientia,Series A. 2018, 38 (1):  156-167.  Abstract ( 126 )   RICH HTML PDF (334KB) ( 86 )   Save The objective of this paper is to research the model of structured bacterial populations with generalized boundary condition in L1 space, It is discussed that the irreducibility of the generated C0 positive semigroup and the spectral analysis of the transport operator for this model, It is to obtain that the asymptotic behavior of the transport equation's solution in the uniform topology, which allows us to describe the asynchronous growth property of the studied bacterial population and so on. References | Related Articles | Metrics

Select

Quenching Solution for Nonlinear Heat Equation with Opposite Absorption Sources and Its Simulation Niu Yi, Peng Xiuyan, Wang Xingchang, Yu Tao, Yang Yanbing Acta mathematica scientia,Series A. 2018, 38 (1):  168-173.  Abstract ( 120 )   RICH HTML PDF (347KB) ( 113 )   Save In this paper, we consider initial boundary value problems for a class of nonlinear reaction-diffusion equations with both a positive and negative absorption sources. We obtain the quenching phenomenon of the above problem, and estimate its quenching time. Further, we simulate by the MATLAB. References | Related Articles | Metrics

Select

Existence of Periodic Solution of Holling-Tanner System with State Feedback Impulsive Control Liang Zhiqing, Zeng Xiaping, Zhou Zewen, Pang Guoping, Huang Junhua Acta mathematica scientia,Series A. 2018, 38 (1):  174-189.  Abstract ( 166 )   RICH HTML PDF (8796KB) ( 107 )   Save In this paper, we investigate the Holling-Tanner model with state feedback impulsive control. On the premise that the continuous system has a unique limit cycle and the positive equilibrium point is an unstable focus point, by means of the geometry theory of semi-continuous dynamic system, successor function method and mathematical analysis method, we obtain sufficient conditions for the existence, uniqueness and orbital stability of order 1 periodic solution of the impulsive system. The main conclusions are verified by numerical simulation. Moreover, the numerical results show that the impulsive system has order k periodic solutions within the limit cycle for some parameters. References | Related Articles | Metrics

Select

Study of Nonlinear Duffing Disturbed Oscillator for Resonance Mechanism Ouyang Cheng, Mo Jiaqi Acta mathematica scientia,Series A. 2018, 38 (1):  190-196.  Abstract ( 126 )   RICH HTML PDF (361KB) ( 70 )   Save A class of nonlinear generalized Duffing disturbed mechanism is considered. The typical Duffing oscillator for resonance mechanism was found. Using the functional mapping method for the problem, a iteration of asymptotic solutions was constructed. Firstly, the initial approximate function of the Duffing model was obtained. Next, applied iteration relation, the arbitrary times asymptotic solutions to the model were solved successively. Then for a example, the generalized Duffing disturbed oscillator for stochastic resonance mechanism by using the functional homotopic mapping method was simple and valid. Finally, the importance foe the obtained asymptotic solutions was illustrated. References | Related Articles | Metrics

Select

Threshold Dynamical Behaviors of a Stochastic SIS Epidemic Model with Nonlinear Incidence Rate Zhang Liping, Zhao Yu, Yuan Sanling Acta mathematica scientia,Series A. 2018, 38 (1):  197-208.  Abstract ( 155 )   RICH HTML PDF (768KB) ( 92 )   Save In this paper, a stochastic susceptible-infected-susceptible (SIS) epidemic model with nonlinear incidence rate is considered to investigate the effect of environment fluctuation on the transmission threshold dynamical behaviors. By using Feller's test and stochastic comparison principle, we obtain the stochastic basic reproduction number R0s, which determined whether the disease persistent or not. If R0s<1, the disease will go to extinction. If R0s=1, the disease will also go to extinction in probability, which has not been reported in the known literatures. In addition, if R0s>1, the disease will stochastic persistence and the scale range estimation of spread is presented eventually. Finally, numerical simulations are carried out to support the theoretical results. According to the actual parameter, it illustrated the environmental fluctuation have different effect on different size of group. References | Related Articles | Metrics