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25 September 1994, Volume 14 Issue 3 Previous Issue    Next Issue

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THE GLOBAL SMOOTH SOLUTION FOR HIGH-DIMENSIONAL HYPERBOLIC SYSTEMS Hu Zhiming, Zhang Tong Acta mathematica scientia,Series B. 1994, 14 (3):  241-251.  Abstract ( 40 )   RICH HTML PDF (531KB) ( 33 )   Save The Cauchy problem of high-dimensional hyperbolic systems of nonlinear equations with initial data have been considered. Under certain assumptions on the eigenvalues of the nonlinear systems and the initial data,we get two theorems about the existence of global smooth solutions. Related Articles | Metrics

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GENERALIZATIONS OF GENERALIZED BI-QUASI-VARIATIONAL INEQUALITIES Ding Xieping Acta mathematica scientia,Series B. 1994, 14 (3):  252-260.  Abstract ( 50 )   RICH HTML PDF (515KB) ( 32 )   Save Let E.F be topological vector spaces over the field Φ(which is either the real field R or the complex field C).let<,>:=F×E→Φ be a bilinear functional.and let X be a nonempty subset of E.Given a multi-valued map S:X→2x,two multi-valued maps M.T:X→2F and a function h:X×X→ R, the generalized bi-quasi-variational inequality problem (GBQVIP)is to find a point ŷ ∈ X such that ŷ∈S(ŷ) and infw∈T(ŷ).Re(f-w,ŷ-x) + h(ŷ,x) ≤ 0 for all x ∈ S(ŷ) and for all f ∈M(ŷ).In this paper,we obtain three general existence theorems on solutions of GBQVIPs which simultaneously unify,sharpen and extend the corresponding results of Shih-Tan and Zhou-Chen to paracompact setting. Related Articles | Metrics

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INITIAL VALUE PROBLEM FOR A NONLINEAR SINGULAR INTEGRO-DIFFERENTIAL EQUATION Zhang Linghai Acta mathematica scientia,Series B. 1994, 14 (3):  261-271.  Abstract ( 58 )   RICH HTML PDF (589KB) ( 28 )   Save The author studies the initial value problem for a nonlinear singular integro-differential equation.By means of Leray-Schauder's fed point principle and some a priori estimates of the solutions of the mentioned problem,he demonstrates the existence and uniqueness theorems of the generalized and classical global solutions of the problem. Related Articles | Metrics

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THE APPROXIMATION THEOREM OF STOCHASTIC DIFFERENTIAL EQUATIONS IN THE PLANE Long Hongwei Acta mathematica scientia,Series B. 1994, 14 (3):  272-282.  Abstract ( 41 )   RICH HTML PDF (548KB) ( 29 )   Save In this paper,we consider the approximation problem of stochastic differential equation with respect to two-parameter Wiener processes and deal with the relation between the solution of stochastic differential equation dXn=σ(Xn)dBz+(1)/4σσ'(Xn) dz and the solution of ordinary differential equation dXn(z)=σ(Xn(z)dBzn,where Bzn is a special sequence of approximation to Bz. Related Articles | Metrics

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NEWTON-KANTOROVICH ITERATION METHOD FOR SOLVING INVERSE PROBLEMS OF NONLINEAR PARABOLIC SYSTEMS Yu Wenhuan Acta mathematica scientia,Series B. 1994, 14 (3):  283-296.  Abstract ( 67 )   RICH HTML PDF (763KB) ( 31 )   Save We consider to identify the parameters.which are functions of spatial and or time variables,in a quasi-linear parabolic equation.First,we prove that the solution of the parabolic equation is a smooth function with respect to the parameters,and then we give a modified Newton-Kantorovich iteration regularity method(NKR) to construct the solution of the inverse problem of the partial differential equation.Secondly,we give a proof of convergence for NKR. Finally,we give a computational example to show that the sequence generated by NKR does converge to the real solution of the inverse problem when the initial guess is close to it. Related Articles | Metrics

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MULTIPLE POSITIVE SOLUTIONS OF INHOMOGENEOUS SEMILINEAR ELLIPTIC EQUATIONS IN UNBOUNDED DOMAINS IN R2 Cao Dao-Min Acta mathematica scientia,Series B. 1994, 14 (3):  297-312.  Abstract ( 65 )   RICH HTML PDF (837KB) ( 32 )   Save In this paper,we consider the existence of multiple positive solutions of the following inhomogeneous semilinear elliptic equation -△u+u=λ(f(u)+h(x)) in Ω u∈H01(Ω),u>0 in Ω (P)λ where λ> 0,Ω=w and ω is a bounded smooth open set in R2,h(x)∈ L2(Ω),h(x)≢0,f(t)∈ C1([0,+∞)) satisfies f(0)=f'(0)=0,fw(t) exists and fw(t)> 0,0 < f(t) < Cexp(αtn) for some constants C,α> 0.0 < v < 2 and t∈(0,+∞),f(t)<θtf'(t) for some θ ∈(0,1). By looking for the local minimum of the corresponding energy functional we tain the first minimum positive solution and by applying mountain pass lemma around the ndboum positive solution we prove the following result: Theorem (P)λ has at least two positive solutions if λ∈(0,λ*) whcre λ*> O is some constant and (P)λ has no positive solution if λ > λ*. Related Articles | Metrics

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A THEOREM ON EMBEDDING Ws,p INTO L(np)/n-sp,P Jiang Ming Acta mathematica scientia,Series B. 1994, 14 (3):  313-317.  Abstract ( 52 )   RICH HTML PDF (268KB) ( 31 )   Save It is proved that Ws,p is continuously embedded into L(np)/n-sp,P for s> 0,p ≥ 1,and n ≥ 1,if n>sp. Related Articles | Metrics

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ON THE LOCAL SOLVABILITY OF DIFFERENTIAL EQUATIONS ASSOCIATED TO UNSOLVABLE INHOMOGENEOUS LEFT INVARIANT DIFFERENTIAL OPERATORS ON THE HEISENBERG GROUP Cui Shanghai Acta mathematica scientia,Series B. 1994, 14 (3):  318-328.  Abstract ( 56 )   RICH HTML PDF (635KB) ( 28 )   Save This paper studies the local solvability of the differential equations associated to unsolvable inhomogeneous left invariant differential operators on the Heisenberg group.It is proved that for a class of inhomogeneous left invariant differential operators on the Heisenberg group,the local solvability of the corresponding equations is equivalent to the local sovability of the equations associated to their highest order terms.Then,under certain conditions on the highest order term,we obtain the necessary and sufficient conditions for the functon f to satisfy ill order for the differential equation Lu=f to be locally solvable. Related Articles | Metrics

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ADMISSIBILITY FOR LINEAR ESTIMATES ON REGRESSION COEFFICIENTS IN A GENERAL MULTIVARIATE LINEAR MODEL Xie Minyu Acta mathematica scientia,Series B. 1994, 14 (3):  329-337.  Abstract ( 53 )   RICH HTML PDF (496KB) ( 30 )   Save In this paper,we discuss admissibility for linear estimates on regression coefficients in a general multivahate linear model.Eight kinds of definition for admissibility are given.We have proved that they can be divided into three identical subclassed in the class of linear estimates,and got necessary and sufficient conditions for admissible estimates on each subclass.Particularly.the eight kinds of admissibility are identify under a special case of the model. Related Articles | Metrics

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CERTAIN SUBCLASSES OF ANALYTIC p-VALENT FUNCTIONS FOR OPERATORS ON HILBERT SPACE Jian Ming Acta mathematica scientia,Series B. 1994, 14 (3):  338-347.  Abstract ( 55 )   RICH HTML PDF (547KB) ( 29 )   Save In this paper,We mainly discuss some subclasses of analytic functions for operators on H, and determine a representation formula and sufficient condition for the class Φp*(α,β,γ,ε,η) and prove a sufficient and necessary condition.coefficient estimates and distortiontheorem for the subclass Φp0*(α,β,γ,ε,η) of the class Φp*(α,β,γ,ε,η).Furthermore,the analogues also are true for operators on Hilbert space. Related Articles | Metrics

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FINITE NEAREST PARTICLE SYSTEMS ON A TREE Chen Dayue Acta mathematica scientia,Series B. 1994, 14 (3):  348-353.  Abstract ( 41 )   RICH HTML PDF (338KB) ( 35 )   Save In this paper we construct finite reversible nearest particle systems on a tree.Using the Dirichlet principle we prove that the finite reversible nearest particle system exhibits a phase transition Related Articles | Metrics

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ON INCLUSION RELATIONS BETWEEN BERS-ORLICZ SPACES Zhao Ruhan Acta mathematica scientia,Series B. 1994, 14 (3):  354-360.  Abstract ( 59 )   RICH HTML PDF (351KB) ( 30 )   Save In this paper the necessary and sufficient condition that a Bers-Orlicz space belongs to the space of bounded automorphic forms is given,and some inclusion relations between Bers-Orlicz spaces is studied. Related Articles | Metrics