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  existence and uniqueness
       On the existence and uniqueness theorems of solutions for the systems of mixed monotone operator equations with applications
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       On the existence and uniqueness of positive solutions for a class of degenerate elliptic systems
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       The existence and uniqueness of the positive solution of such a system are proved.
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       Existence and uniqueness results are established via theLp-Lq a priori estimates and the inverse function theorem.
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       The existence and uniqueness of a global smooth solution of this system with Cauchy problem and its stability and time decay rate are studied by means of an elementary energy method.
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  existence uniqueness
       Existence uniqueness and asymptotic stability of periodic solutions of a nonlinear equation in phase locked technology
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       After proving the existence uniqueness of interpolation problems at center, vertex and partial center, we give the construction methods for these three interpolatiny functions.
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       By applying a minimax inequality obtained by the author, some existence uniqueness theorems of solutions for the mixed nonlinear variational-like inequalities are proved.
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       These are shown to be related by the Abel transform and an existence uniqueness theorem is presented.
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       This paper proves local existence uniqueness and smoothness properties and improves, by essentially one order of differentiability, previous local existence results.
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  unique existence
       The problems of the unique existence and computation of a Nash equilibrium are studied for these models.
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       MacPherson posed the problem of unique existence of a bivariant Chern class—a Grothendieck transformation from the bivariant theory F of constructible functions to the bivariant homology theory H.
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       Using the method of dynamic potentials, the theorems of the unique existence of the solution are proved.
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       Unique existence of periodic solutions of neutral Volterra integrodifferential equations
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       Necessary and sufficient condition for the unique existence of periodic solution of linear volterra equations
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  the existence and uniqueness
       On the existence and uniqueness theorems of solutions for the systems of mixed monotone operator equations with applications
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       On the existence and uniqueness of positive solutions for a class of degenerate elliptic systems
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       The existence and uniqueness of the positive solution of such a system are proved.
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       The existence and uniqueness of a global smooth solution of this system with Cauchy problem and its stability and time decay rate are studied by means of an elementary energy method.
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       In this paper, the existence and uniqueness of solutions for boundary value problemx?=f(t, x, x', x″),x(0)=A,x'(0)=B,g(x'(1),x″(1))=0 are studied by using Volterra type operator and upper and lower solutions.
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  其他



         Consider the real differential system dx/dt=P_3(x,y), dy/dt=Q_3(x,y)where P_3(x,y) and Q_3(x,y) are polynomials of the 3-rd degree. Suppose that the system has at lease one elementary critical point of index+1, and it can be written in the form dx/dt=-y+xF_1(x,y)+gy~2+hy~2 (1) dy/dt-x+yF_2(x,y)+rx~2+sx~3 where F_1(x,y)and F_2(x,y) are polynomials of the 2-nd degree. If g=h=r=s=0 and F_1(x,y)≡F_2(x,y), then systen(1)takes the form dx/dt=-y+xF(x,y),dy/dt=x+yF(x,y) (2)for which we have the following: Theorem. ...
            討論题目中P_3(x,y)与Q_3(y,x)是具实系数的三次多項式时的方程組的週期解与极限环問题。設方程組至少有一指标为+1的初等奇点且可写成下列形式 dx/dt=-y+xF_1(x,y)+gy~2+hy~3,dy/dt=x+yF_2(x,y)+rx~2+sx~3其中,F_1(x,y)与F_2(x,y)均为二次多項式。当g=h=r=s=0时,在F_1(x,y)≡F_2(x,y)或F_2(x,y)≡0的假設下,就上列方程組建立了极限环的存在唯一性定理。此外,对上列方程組本身以及其他一些特殊情况分別給出了存在极限环或不存在週期解的充分性条件。
文摘来源
         We use the theory of cubic equations and the Tychonoff fixed point
            本文运用三次代数方程及不动点定理等方法研究非线性微分差分方程x’(t)+αx(t)-αcx(t-τ)+g〔αx~3(t)+3x~2(t)x’(t)〕=0 的解的存在唯一性问题。此外,还讨论了解的稳定性,当τ→0时解的性态及周期解的不存在问题。非线性微分差分方程x’(t)+αx(t)-αcx(t-τ)+g(αx~3(t)+3x~2(t)x’(t)〕=0(1)是在研究具时滞的非线性振荡电路时产生.这里,α,c,g都是实的常数,α>0,“’”代表d/dt。我们来研究(1)的解的性态和周期解的问题。作者对胡金昌教授的审阅指导表示衷心感谢。
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         ~~
            本文研究了特征方程有一对复重根的常系数二阶两个自变数两个未知函数的线性椭圆型微分方程组(1 0 0 λ)~2/x~2(u v)+(0 λ-1 λ-1 0)~2/xy(u v)+(λ 0 0 1)~2/y~2(u v)=0,(λ≠0,1)的Neumann问题等三类边界问题的解的存在唯一性
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