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08 September 2000, Volume 20 Issue 4 Previous Issue    Next Issue

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An Existence Theroem on a Class of Nonlinear Schrodinger Equations with Periodical and Sign-Changing Potentials Liu Xiaochun Liu Xiaochun Acta mathematica scientia,Series A. 2000, 20 (4):  433-444.  Abstract ( 690 )   RICH HTML PDF (390KB) ( 679 )   Save In this paper, we discuss one class of nonlinear Schrodinger equations with periodical and sign-changing potentials. We use the Lyapunov-Schmidt reduction method and concentrationcompactness principle to get the existence of a weak solution. Key words Schrodinger operators, Concentration compactness, Periodical and sign-changing potentials. References | Related Articles | Metrics

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Oscillatory and Asymptotic Behavior of Solutions for Second Order Functional Differential Equations with Forcing Term Yu Yuanhong Fang Hui Zhou Yong Acta mathematica scientia,Series A. 2000, 20 (4):  445-450.  Abstract ( 1074 )   RICH HTML PDF (307KB) ( 850 )   Save In this paper several oscillatory and asymptotic properties of solutions for second order functional differential equations with deviating arguments depend on the state itself are established. Results obtained generalize and improve those in the literature. References | Related Articles | Metrics

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On SquareRooting Matrices of the Jordan Matrices Jm1(λ1)⊕Jm2(λ2) Zhu Degao Acta mathematica scientia,Series A. 2000, 20 (4):  451-460.  Abstract ( 817 )   RICH HTML PDF (320KB) ( 708 )   Save J=Jm1(λ1)⊕Jm2(λ2) is the Jordan normal form which has two Jordan blocks Jm1(λ1) and Jm2(λ2).J has square-rooting matrices iff one of following holds: (i) λ1,λ2≠0; (ii)λ1=0, but λ2≠0, then m1=1, or λ1≠0, but λ2=0, then m2=1; (iii) λ1=λ2=0, then m1=m2,m1+1=m2 or m2+1=m1.And we give the expresses of square-rooting matices of J. References | Related Articles | Metrics

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On a Nonlinear Elliptic Equation with Sublinear Term at Origin Sun Yijing Wu Shaoping Acta mathematica scientia,Series A. 2000, 20 (4):  461-467.  Abstract ( 789 )   RICH HTML PDF (340KB) ( 790 )   Save This paper deals with a class of semilinear elliptic Dirichlet boundary value problems with the sign-changing or negative coefficient funtion for concave nonlinearities of the form |u|q-2u,1<q<2, to establish some existence and multiplicity results. References | Related Articles | Metrics

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Linear Admissible Estimators of Regression Coefficient Under Balanced Loss Xu Xingzhong Wu Qiguang Acta mathematica scientia,Series A. 2000, 20 (4):  468-473.  Abstract ( 737 )   RICH HTML PDF (340KB) ( 911 )   Save In this paper, we study the admissibility of linear estimators of regression coefficient in linear model under balanced loss function. The necessary and sufficient condition that a linear estimator is admissible among linear estimator class is given. It shows that linear admissible estimators are also balance of estimators. References | Related Articles | Metrics

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A Liouville Theorem for a Class of Nonlinear Elliptic Equations Hu Zejun Acta mathematica scientia,Series A. 2000, 20 (4):  474-479.  Abstract ( 744 )   RICH HTML PDF (327KB) ( 775 )   Save Let (Mn, g) be a complete Riemannian manifold of dimention n with Ricci curvature RicM(x)≥-A(1+r2(x)ln2(2+r(x))), where A is a nonnegative constant and r(x) is the geodesic distance from x to some fixed point x0∈M.\$ In this paper, we show that there is no nonnegative C2 solution but zero to the equation Δu+Su+Kuα=0 on M under such conditions as: S≤0 on M; K<0 on M and K≤-a2<0 outside some compact set for a constant a>0 and any constant α>1. References | Related Articles | Metrics

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General Integrated Semigroups Shen Junhao Song Guozhu Acta mathematica scientia,Series A. 2000, 20 (4):  480-486.  Abstract ( 770 )   RICH HTML PDF (340KB) ( 869 )   Save In this paper we difine the concept of general ingegrated semigroup.The generator and genaration of this general integrated semigroup are discussed. Also, some examples and applications are given. References | Related Articles | Metrics

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Existence of Positive Solution for a Semilinear Elliptic Equation Involving Nearly Critical Exponent Yao Yangxi Xu Jinghua Yao Ruohe Acta mathematica scientia,Series A. 2000, 20 (4):  487-492.  Abstract ( 873 )   RICH HTML PDF (309KB) ( 791 )   Save  This paper deals with a semiliear elliptic equation involving nearly critical Sobolev exponent. We prove that for each strictly local maximun point x0 of he related Green's function, the problem has a positive solution,concentrating at x0. References | Related Articles | Metrics

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Topological Quantum Field Theory and Crossing Number Zheng Zhujun Wu Ke Wang Shikun Hu Jianxun Acta mathematica scientia,Series A. 2000, 20 (4):  493-498.  Abstract ( 719 )   RICH HTML PDF (319KB) ( 1082 )   Save  In this paper,we construct a new topological quantum field theory of cohomological type and show that the partition function is a crossing number. References | Related Articles | Metrics

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Genric Oscillation of Higher Order Delay Differential Equation Feng Wei Duan Yongrui Yan Jurang Acta mathematica scientia,Series A. 2000, 20 (4):  499-505.  Abstract ( 739 )   RICH HTML PDF (351KB) ( 889 )   Save In this paper, we study the generic oscillation and generic nonoscillation of higher order delay differential equation y(n)(t) + py′(t) + qy(t-τ)=0. We provide sufficient conditions for generic oscillation and generic nonoscillation of this kind of equation. References | Related Articles | Metrics

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Global Solutions of a Class of Nonlinear Integrodifferential Equations in Banach Spaces Chen Fangqi1,2 Chen Yushu2 Wu Zhiqiang2 Acta mathematica scientia,Series A. 2000, 20 (4):  506-512.  Abstract ( 921 )   RICH HTML PDF (338KB) ( 719 )   Save The existence of global solutions and coupled minimal and maximal quasisolutions are studied for a class of nonlinear integrodifferential equations on the infinite interval R+ in Banach spaces. Some existence theorems of global solutions and coupled minimal and maximal quasisolutions are obtained which improve and generalize the related results in [1-2]. References | Related Articles | Metrics

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The Continuity of NonArbitrage Budget Correspondence He Sui Acta mathematica scientia,Series A. 2000, 20 (4):  513-520.  Abstract ( 744 )   RICH HTML PDF (351KB) ( 833 )   Save The budget constraints with imcomplete markets are nonlinear setvalued mappings from product space of price simplex and Grassman manifold to commodity space when consumers' preferences are convex. In order to study the existence of general equilibrium in this modle, we investigated the set-valued mappings and proved that nonarbitrage budget correspondences are continuous. References | Related Articles | Metrics

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Percolation Model on Lattice Nested Fractals Lu Jiansheng Acta mathematica scientia,Series A. 2000, 20 (4):  521-527.  Abstract ( 862 )   RICH HTML PDF (362KB) ( 747 )   Save This paper will study the percolation model on one kind of lattice fractals(lattice nested fractals), prove that there is no critical phenomenon for this percolation model and give one law of exponent decay. Moreover, it will prove that there is no critical phenomenon for bond percolation model on finite branched graph. References | Related Articles | Metrics

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A Harmonic Calculus on SG(N,3) Li Junping Hou Zhenting Acta mathematica scientia,Series A. 2000, 20 (4):  528-539.  Abstract ( 777 )   RICH HTML PDF (380KB) ( 710 )   Save In this paper, We discussed harmonic calculus on fractal spaces SG(N,3),and obtained the harmonic functions,the existence and uniqeness theorem of the solutions to Dirichlet and Neumann problems on SG(N,3),further more, the Gauss-Green formula was also given. References | Related Articles | Metrics

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On Common Borel Points of a Meromorphic Function and its Differential Polynomial in the Unit Circle Wu Guirong Pan Biao Acta mathematica scientia,Series A. 2000, 20 (4):  540-546.  Abstract ( 969 )   RICH HTML PDF (324KB) ( 693 )   Save Let f be a meromorphic function of finite positive order in the unit circle and F be a differential polynomial in f, If the order of growth of F is same as that of f, then the Borel points of F must be the Borel points of f. In particular the Borel points of a monomial in f are also the Borel points of f under certain conditions. In addition, A result on orders of homogeneous differential polynomial due to Singh,A.P.is generalized. References | Related Articles | Metrics

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Existence of Multiple Solutions for a Semilinear Biharmonic-Equation with Critical Exponent Zeng Xianzhong Deng Yinbin Acta mathematica scientia,Series A. 2000, 20 (4):  547-554.  Abstract ( 843 )   RICH HTML PDF (367KB) ( 822 )   Save This paper gives the existence and nonexistence of multiple solutions for the problem: Δ2u=λu+|u|p-1u+μf(x), x∈Ω,μ>0; u|Ω=0, u/n| Ω=0. Where Ω is a smooth bounded domain in RN,λ∈R,μ>0,p=(N+4)/(N-4),N≥5,f(x) is a given nonnegative function. References | Related Articles | Metrics

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The Existence of Entire Solutions of Some Elliptic System in Rn Xue Ruying Acta mathematica scientia,Series A. 2000, 20 (4):  555-561.  Abstract ( 984 )   RICH HTML PDF (335KB) ( 839 )   Save We consider the existence and the asymptotic properties of entire solutions of some elliptic system in Rn. Some sufficient conditions which ensure the existence of entire solutions are given in this paper. References | Related Articles | Metrics

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On the Borel Points of Quasi-Meromorphic Mappings in the Unit Circle Deng Fangwen Acta mathematica scientia,Series A. 2000, 20 (4):  562-567.  Abstract ( 744 )   RICH HTML PDF (312KB) ( 806 )   Save We study quasi-meromorphic mappings in the unit cirde and build inequalities on the angular domains, then the existence of Borle points of quasi-meromorphic mappings in proned. References | Related Articles | Metrics

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On the Riest Basis Property of a Hybrid System with Boundary Feedback Control Yao Cuizhen Acta mathematica scientia,Series A. 2000, 20 (4):  568-576.  Abstract ( 1038 )   RICH HTML PDF (367KB) ( 740 )   Save An Euler-Bernoulli beam equation with one end fixed and a tip mass at another end is considered. It is shown that the closedloop system under boundary linear feedback control is a riesz spectral system. That is, there is a sequence of generalized eigenfunctions, which forms a riest basis for the state Hilberf space. The spectrum－determined growth condition is hence established. In the meanwhile, the asymptotic expansion of the eigenvolues is derived and the exponential seability of the system is concluded. References | Related Articles | Metrics