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26 June 2016, Volume 36 Issue 3 Previous Issue    Next Issue

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The Algebroid Functions with Given Borel Directions Zhang Shaohua, Liu Huifang, Sun Daochun Acta mathematica scientia,Series A. 2016, 36 (3):  401-412.  Abstract ( 95 )   RICH HTML PDF (345KB) ( 624 )   Save Algebroid functions are multi-valued function that generally determined by the irreducible binary complex equations. There exists some difficulties in verifying the irreducible of such equations, and the irreducible binary complex equations may be reducible in the local domain. Hence in this paper, we investigate the properties of the algebroid functions defined by the binary complex equations (not necessarily irreducible) in the disc. And by using the obtained properties, we construct the infinite order algebroid functions with given Borel directions. References | Related Articles | Metrics

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Maps Preserving Partial Isometries of Operator Pencils Wei Yanan, Ji Guoxing Acta mathematica scientia,Series A. 2016, 36 (3):  413-424.  Abstract ( 163 )   RICH HTML PDF (339KB) ( 174 )   Save Let B(H) be the algebra of all bounded linear operators on a complex Hilbert space H, PI(H) the set of all partial isometries in B(H). It is proved that a surjective map Φ on B(H) preserves partial isometries of pencils of operators, that is, A-λB∈PI(H)⇔Φ(A)-λΦ(B)∈PI(H) if and only if there are two unitary operators U and V on H such that Φ(X)=UXV for all X in B(H) or there are two anti-unitary operators U and V on H such that Φ(X)=UX*V for all X in B(H). References | Related Articles | Metrics

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Normality Concerning Shared Functions Yang Duanyang, Ye Yasheng Acta mathematica scientia,Series A. 2016, 36 (3):  425-432.  Abstract ( 133 )   RICH HTML PDF (270KB) ( 188 )   Save Let k be a positive integer, a(z)(0,∞) be meromorphic functions on a domain D, F be a family of meromorphic functions on D, all of whose zeros have multiplicity at least k. If, for each f∈F, f(z)=0⇔f(k)(z)=a(z)⇒0<|f(k+1)(z)-a'(z)|<|a(z)|, then F is normal on D. References | Related Articles | Metrics

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Generalized Roper-Suffridge Extension Operators and Loewner Chains Wang Chaojun, Cui Yanyan, Liu Hao Acta mathematica scientia,Series A. 2016, 36 (3):  433-440.  Abstract ( 122 )   RICH HTML PDF (285KB) ( 150 )   Save In this paper, we mainly seek conditions under which a kind of generalized Roper-Suffridge operators can be embedded in Loewner chains. Sequentially, by the analytical characteristics of almost spirallikeness of order α and type β, we discuss the generalized Roper-Suffridge operators preserve almost spirallikeness of order α and type β on a bounded and completely Reinhardt domain. The conclusions generalize the previous results. References | Related Articles | Metrics

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Phragmén-Lindelöf Type Theorems in a Generalized Strip Qiao Lei Acta mathematica scientia,Series A. 2016, 36 (3):  441-447.  Abstract ( 101 )   RICH HTML PDF (281KB) ( 157 )   Save In this paper, we give the Phragmén-Lindelöf type theorems in a generalized strip, which generalized the results obtained by Deng and Aikawa in a strip. References | Related Articles | Metrics

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Complete Convergence for Weighted Sums Under END Setup Li Wei Acta mathematica scientia,Series A. 2016, 36 (3):  448-455.  Abstract ( 122 )   RICH HTML PDF (290KB) ( 124 )   Save The complete convergence for the weighted sums of identically distributed NA random variables in [1] is improved and extended under the END setup. The main tool in [1] is the maximum Rosenthal's type moemnt inequality, but it is unknown whether the kind of moment inequality holds or not for END, so our method is different from [1]. References | Related Articles | Metrics

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The Weighted Poincaré Inequality in the Upper Half Space of Nilpotent Lie Group Lian Baosheng, Shen Xiaoyu, Xu Yanbing Acta mathematica scientia,Series A. 2016, 36 (3):  456-461.  Abstract ( 113 )   RICH HTML PDF (267KB) ( 120 )   Save In this paper, a class of weighted Poincaré inequality is established in the upper half space of Nilpotent Lie group, and it is proved that the constant is the best. References | Related Articles | Metrics

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Oscillation of Neutral Impulsive Hyperbolic Systems with Deviating Arguments Ma Qingxia, Liu Anping Acta mathematica scientia,Series A. 2016, 36 (3):  462-472.  Abstract ( 168 )   RICH HTML PDF (362KB) ( 64 )   Save Oscillatory properties of systems of neutral type impulsive hyperbolic equations with several deviating arguments under the Robin boundary condition and the Dirichlet boundary condition are investigated, and several new sufficient conditions for oscillation are presented. The main results are illustrated by one example. References | Related Articles | Metrics

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Solvability of a Perturbed Variational Inequality Li Zejun, Sun Shuqin Acta mathematica scientia,Series A. 2016, 36 (3):  473-480.  Abstract ( 153 )   RICH HTML PDF (295KB) ( 113 )   Save The solvability of a perturbed variational inequality is investigated under certain coercivity conditions in this paper. Two main results are obtained. The coercivity condition (B) assumed in the first result implies the solution set of the variational inequality is nonempty and bounded, and the coercivity condition (F) in the second one shows the solution set of the variational inequality is contained in a closed ball. The first result extends some known results, while the second one is new. References | Related Articles | Metrics

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The Gradient Estimates of Laplace Equations with Oblique Boundary Value Problem Xiang Ni, Shi Juhua, Xu Jinju, Wu Yan Acta mathematica scientia,Series A. 2016, 36 (3):  481-492.  Abstract ( 100 )   RICH HTML PDF (330KB) ( 112 )   Save In this paper, the authors study two proofs for the gradient estimates of the Laplace equations with oblique boundary value condition. For the first proof, the gradient estimates of Lieberman[1] are rearranged; for the second proof, barrier function which is different from [1] is used to obtain the gradient estimates. They both use the property of the maximum value point, and get the near boundary gradient estimates and boundary gradient estimates, combining the given inner gradient estimates in [2], and then they obtain the global gradient estimates. References | Related Articles | Metrics

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Morse Indices and Liouville Type Theorems for Weighted Elliptic Equations Xiao Yingying, Zheng Xiongjun Acta mathematica scientia,Series A. 2016, 36 (3):  493-499.  Abstract ( 164 )   RICH HTML PDF (276KB) ( 217 )   Save This paper is concerned with Liouville type theorems for weighted semilinear elliptic equations -Δu=|x|α|u|p-1u,x∈RN and -Δu=|x|α|u|p-1u,x∈R+N,u|∂R+N=0, where N ≥ 3 and α>-2. We prove that the bounded solutions of the above problems with finite Morse indices are zero when 1 < p < (N+2α+2)/(N-2). References | Related Articles | Metrics

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Positive Solutions of Perturbation Elliptic Equation Involving Hardy Potential and Critical Sobolev-Hardy Exponent Zhang Jing Acta mathematica scientia,Series A. 2016, 36 (3):  500-506.  Abstract ( 110 )   RICH HTML PDF (274KB) ( 72 )   Save In this paper, we are concerned with the following elliptic equation involving critical Sobolev-Hardy exponent -Δu-μ(u)/(|x|2)+λa(x)uq=(|u|2*(s)-2)/(|x|s)u,x∈RN,(0.1) u>0,u∈D1,2(RN), where 2*(s)=(2(N-s))/(N-2) is the critical Sobolev-Hardy exponent, N ≥ 3, λ∈R, 0 ≤ s < 2, 1 < q < 2*-1, 0 ≤ μ < μ=((N-2)2)/(4), a(x)∈C(RN). We firstly use an abstract perturbation method in critical point theory to obtain the existence results of positive solutions of the equation for small value of|λ|. Secondly, we focus on an anisotropic elliptic equation of the form  -div[(1+λb(x))▽u]+λa(x)uq=μ(u)/(|x|2)+(|u|2*(s)-2)/(|x|s)u,x∈RN,(0.2) u>0,u∈D1,2(RN), The same abstract method is used to yield existence result of positive solutions of the equation for small value of |λ|. References | Related Articles | Metrics

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Nehari Method to Solutions for a Class of Quasilinear Schrödinger Equations in RN Li Jing, Chen Caisheng Acta mathematica scientia,Series A. 2016, 36 (3):  507-520.  Abstract ( 160 )   RICH HTML PDF (358KB) ( 133 )   Save We consider the existence of positive solutions to a class of quasilinear Schrödinger equations with a parameter. By the Nehari argument and Schwarz symmetrization method, the existence of solutions in two different cases is established. References | Related Articles | Metrics

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Variational Approach to Existence of Weak Solutions to Second-Order Singular Impulsive Problems Liu Jian, Zhao Zengqin Acta mathematica scientia,Series A. 2016, 36 (3):  521-530.  Abstract ( 139 )   RICH HTML PDF (300KB) ( 160 )   Save In this paper, we consider the existence of weak solutions for a class of nonlinear singular impulsive boundary value problems with disturbance term. We obtain some new existence theorems of solutions by using variational methods combing with some critical-point theorems. References | Related Articles | Metrics

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Extinction and Non-Extinction Behavior of Solutions for a Class of Reaction-Diffusion Equations with a Nonlinear Source Zhou Sen, Yang Zuodong Acta mathematica scientia,Series A. 2016, 36 (3):  531-542.  Abstract ( 118 )   RICH HTML PDF (933KB) ( 115 )   Save In this paper, we investigate the extinction and nonextinction behavior of solutions for a class of reaction-diffusion equations. By using the integral model estimates and the method of sub-super solutions, we obtain some sufficient conditions for the solutions vanish in finite time. Furthermore, we also present numerical examples for the sake of illustration. References | Related Articles | Metrics

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Numerical Investigations on Several Stabilized Finite Element Methods for the Navier-Stokes Problem Wen Juan, He Yinnian, Huang Pengzhan, Li Min Acta mathematica scientia,Series A. 2016, 36 (3):  543-557.  Abstract ( 111 )   RICH HTML PDF (4961KB) ( 226 )   Save In this paper, several stabilized finite element methods based on the lowest equal-order finite element pairs (P1/P1 or Q1/Q1) for the steady Navier-Stokes problem are investigated. The methods include penalty, regular, local Gauss integration and multiscale enrichment method. Comparisons among them show that the multiscale enrichment method we constructed is a favorite method in terms of stability and accuracy at higher Reynolds numbers for the Navier-Stokes problem. References | Related Articles | Metrics

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Positive Pseudo Almost Periodic Solutions for a Delayed Nicholson's Blowflies Model with a Feedback Control Huang Zuda Acta mathematica scientia,Series A. 2016, 36 (3):  558-568.  Abstract ( 104 )   RICH HTML PDF (529KB) ( 131 )   Save In this paper, a generalized Nicholson's blowflies model is considered with the introduction of feedback control and multiple time-varying delays. By using Lyapunov functional method and differential inequality techniques, we obtain some sufficient conditions for the existence and global exponential stability of positive pseudo almost periodic solutions of this model. We also provide numerical simulations to support the theoretical results. References | Related Articles | Metrics

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Dynamics of a Predator-Prey System with Impulsive Perturbations and Markovian Switching Zhang Shuwen Acta mathematica scientia,Series A. 2016, 36 (3):  569-583.  Abstract ( 111 )   RICH HTML PDF (399KB) ( 122 )   Save In this paper, a stochastic delay predator-prey system with Markovian switching and impulsive perturbations is studied. We establish conditions for the existence of a global positive solution for the considered system. The superior limit of expectations for the solution of this system is estimated. Afterwards we obtain certain asymptotic results regarding long-time behavior of trajectories of the solution and prove stochastically ultimately boundedness of the system. Furthermore, by constructing a suitable Lyapunov function and using comparison theorem of stochastic differential equation, a set of sufficient conditions for extinction, non-persistence in the mean for every positive solution of the system are obtained. Finally, we give the conclusion. References | Related Articles | Metrics

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A Weighted Population Model with Size-Structure: Stability and Optimal Harvesting He Zerong, Yang Lizhi Acta mathematica scientia,Series A. 2016, 36 (3):  584-600.  Abstract ( 141 )   RICH HTML PDF (787KB) ( 141 )   Save This paper is concerned with the stability and optimal harvesting for a size-structured population model with control of newborns, where fertility and mortality depend the density in different ways. A formal equilibrium is derived and existence of unique steady state is shown via a contraction mapping. Some conditions for asymptotical stability and instability are presented by means of characteristic equation. As for the optimal harvesting problem, we cite the tangent-normal cones to establish an optimal feedback policy, and employ the Ekeland's variational principle to prove the existence and uniqueness of optimal strategies. Two examples demonstrate the evolution of the species. References | Related Articles | Metrics