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25 September 1987, Volume 7 Issue 3 Previous Issue    Next Issue

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AN ANALYTICAL-NUMERICAL METHOD FOR A TYPICAL BIFURCATION PROBLEM Rao Chuanxia Acta mathematica scientia,Series B. 1987, 7 (3):  241-246.  Abstract ( 40 )   RICH HTML PDF (368KB) ( 26 )   Save In this paper, the nonlinear two-point boundary value problem u"+λ2eu=0(λ>0),u(0)=0=u(1) which has a secondary bifurcation point is solved by an anlyticnumerical method. The problem was first transformed analytically into finding roots of the trascendental equation 2√2/t ln(t+√t2-1)=λ(t > 1). Then the turning point was obtained numerically, λc=1.87452030182. And the following three cases are all considered:the problem has two solutions, one solution or no solution, when λ < λc, λ=λc, or λ > λc, respectively. The steps for solving the problem and some results of numerical experiments are given in the paper. Related Articles | Metrics

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SCHWARZ ALTERNATING METHOD AND MULTIGRID METHOD Shao Jianping Acta mathematica scientia,Series B. 1987, 7 (3):  247-257.  Abstract ( 37 )   RICH HTML PDF (718KB) ( 32 )   Save In this paper we propose and establish the convergence of several asynchronous parallel algorithms which are defined by combining the Schwarz alternating method with the multigrid method in two ways. In the first we divide the original problem into p related subproblems, then the multigrid method is used to solve these subproblems iteratively. In the second approach we regard the Schwarz iterative method as the smoothing step of multigrid method. All algorithms proposed in this paper can be used on an MIMD computer. Related Articles | Metrics

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ON THE ASYMPTOTIC EXPANSION OF THE SOLUTION OF NON-AUTONOMOUS AND NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS Qin Huashu Acta mathematica scientia,Series B. 1987, 7 (3):  259-272.  Abstract ( 44 )   RICH HTML PDF (807KB) ( 31 )   Save In this paper we will deal with the asymptotic behavior of the solution to a class of non-autonomous and nonlinear differential equations which is more general than the Riccati matrix differential equation. Related Articles | Metrics

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EIGENVALUE THEORY OF STRETCHING FLUID SHEETS Han Shifang Acta mathematica scientia,Series B. 1987, 7 (3):  273-285.  Abstract ( 54 )   RICH HTML PDF (695KB) ( 29 )   Save Using the constitutive equation for slightly disturbed extensional flow[10,11], an eigenvalue theory of stretching fluid sheets has been developed. The present stability analysis is given from the Lagrangean point of view. The dependent variables are written as functions of material particles and time. An equation for the amplitude of the disturbance stream function φ(η, t) is derived. A general eigenvalue theory is discussed to explain the instability of Newtonian and non-Newtonian stretching fluid sheets. For the non-Newtonian fluid case the theory is specialized to a Maxwell model. The present theory predicts the influence of wave number on the stability of stretching fluids. Related Articles | Metrics

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THE EMBEDDED THEOREM AND ITS APPLICATION TO STATISTICAL METRIC SPACE Liu Zhoshu Acta mathematica scientia,Series B. 1987, 7 (3):  287-297.  Abstract ( 39 )   RICH HTML PDF (683KB) ( 33 )   Save We prove the following result in this paper:Let(X, J, △) be a T-complete Menger space. If {Ti, i=1, 2, …} are a sequence of the self mapping of the contractive type on X and {mi(x), i=1, 2, …} are the functional sequence satisfying mi(x)|m(Ti(x)), i=1, 2, …, then {Ti, i=1, 2, …} have a common fixed point. This result is a generalization to the result obtained in I. Istratescu[7, 14]. Other results are proved concerning the fixed point theorems for G-valued metric space. The concept, the embedded theorem of S. M. space, is discussed and its relation to the existence of fixed point for above mapping is also discussed in S. M. space. Related Articles | Metrics

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NONEXISTENCE RESULTS AND EXISTENCE THEOREMS OF POSITIVE SOLUTIONS OF DIRICHLET PROBLEMS FOR A CLASS OF SEMILINEAR ELLIPTIC SYSTEMS OF SECOND ORDER Chen Baoyao Acta mathematica scientia,Series B. 1987, 7 (3):  299-309.  Abstract ( 44 )   RICH HTML PDF (603KB) ( 33 )   Save We consider the following boundary problem of semilinear elliptic systems: (A) -△ul=fl(u1,u2,…,uN)+λul, ul > 0 in Ω, ul on ∂Ω. Related Articles | Metrics

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OVERTAKING OF SHOCKS OF THE SAME KIND IN THE ISENTROPIC STEADY SUPERSONIC PLANE FLOW Chen Guiqiang Acta mathematica scientia,Series B. 1987, 7 (3):  311-327.  Abstract ( 45 )   RICH HTML PDF (889KB) ( 32 )   Save Related Articles | Metrics

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NONTRIVIAL SOLUTIONS OF QUASILINEAR ELLIPTIC EQUATIONS IN W01,p INVOLVING LIMITING NONLINEARITIES Li Gongbao Acta mathematica scientia,Series B. 1987, 7 (3):  329-339.  Abstract ( 44 )   RICH HTML PDF (572KB) ( 35 )   Save In this paper, We get the existence of non-trivial solutions of the following elliptic equations -Σi=1n ∂/∂xi (|▽u|p-2 ∂u/∂xi)=λ|u|p-2u±u|u|p*-2 in Ω⊂Rn, where n > p ≥ 2 and p*=np/(n-p). Related Articles | Metrics

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ON THE EXISTENCE OF NONTRIVIAL SOLUTION OF A QUASILINEAR ELLIPTIC BOUNDARY VALUE PROBLEM FOR UNBOUNDED DOMAINS (Ⅰ) Positive Mass Case Yang Jianfu, Zhu Xiping Acta mathematica scientia,Series B. 1987, 7 (3):  341-359.  Abstract ( 53 )   RICH HTML PDF (1052KB) ( 40 )   Save Related Articles | Metrics