刚性方程组M~.(t)+C~.X(t)+KX(t)=F(t)解的探讨

讨论了刚性常微分方程组(1)的解析解和数值解,给出了解的一般形式和应用该算法的数值例子.     

方程a2(x)(t-τ)+a1(x)(t-τ)+a0x(t-τ)+b2(x)(t)+b1(x)(t)+b0x(t)=δ的部分解讨论

讨论了方程a2(x)(t-τ)+a1(x)(t-τ)+a0x(t-τ)+b2(x)(t)+b1(x)(t)+b0x(t)=δ的部分解.     

中立型方程(·x)(t)+c(·x)(t-τ)+ax(t)+bx(t-τ)=0零解渐近稳定的代数判据

本文建立了方程．．．．零解渐近稳定的充要条件,给出了其零解渐近稳定的代数判据,同时纠正了文（２）中出现的错误。     

方程a_2“非汉字符号”(t-τ)+a_1(t-τ)+a_0x(t-τ)+b_2“非汉字符号”(t)+b_1(t)+b_0x(t)=δ的部分解讨论

讨论了方程 a2 x( t-τ) + a1x( t-τ) + a0 x( t-τ) + b2 x( t) + b1x( t) + b0 x( t) =δ的部分解     

迭代微分方程x'(t)=ω(t)(ax(t)-bx(x(t)))(a>b>0)的周期解

本文讨论了一类非自治迭代微分方程ｘ’（ｔ）＝ω（ｔ）（ａｘ（ｔ）－ｂｘ（ｘ（ｔ）））（ａ＞ｂ＞０）的解的存在性、解的性态及周期．此结论推广了文［１］的定理．     

方程x'(t)=ax(t)+bx(3[(t+1)/3])的数值稳定性分析（英文）

本文研究了分段连续型微分方程x'(t)=ax(t)+bx(3[(t+1)/3])Euler-Maclaurin方法的数值稳定性问题.利用特征分析的方法,获得了数值解稳定的充分条件,进而证明了Euler-Maclaurin方法保持了精确解的稳定性.最后给出了一些数值例子.     

方程(t)+p(t)(t)+q(t)x(t)=0的稳定性

本文应用交换技巧以及直接方法研究了二阶线性系统(1)的平凡解的稳定性,得到若干充分条件、必要条件以及充分必要条件,推广了文献[1—8]中的有关结果。     

u~(4)(t)-λh(t)f(u(t))=0的边值问题的正解存在性

本文考察了边值问题u（4）-λh（t）f（u（t））＝0,0＜t＜1,u（0）=u（1）="（0）=u"（1）=0的正解存在性和多解性,其中λ＞0本文推广了［3］的结论．     

三元三次不定方程ax^(2)+by^(2)+cz^(2)=dxyz-1基础解的进一步研究

关于三元三次不定方程的研究,是不定方程研究中的重要课题,有许多尚未解决的问题.讨论了不定方程ax^(2)+by^(2)+cz^(2)=dxyz-1的基础解,其中(a,b,c)=1,a,b,c均为d的因子.利用文献中的方法,运用二元二次型理论和初等数论的结果,求出了该不定方程的所有基础解.     

关于方程(χ)+RF′(χ)(χ)+1/LF(x)=p(t)的周期解

利用了Mawhin[2]提出的延拓定理,给出的高压输电网设计中的一类方程的周期解的存在性.     

Le soluzioni periodiche dell’equazione differenziale non linearex″(t)+2x 3 (t)=f(t)

Lavoro eseguito nell’ambito del gruppo di ricerca n. 24 del C.N.R.     

The Equation f(X) = f(Y) in Rational Functions X = X(t), Y = Y(t)

We determine all the complex polynomials f(X) such that, for two suitable distinct, nonconstant rational functions g(t) and h(t), the equality f(g(t)) = f(h(t)) holds. This extends former results of Tverberg, and is a contribution to the more general question of determining the polynomials f(X) over a number field K such that f(X) – has at least two distinct K-rational roots for infinitely many K.     

On the Construction of Cosine Operator Functions and Semigroups on Function Spaces with Generator a(x)(d2dx2)+b(x)(d/dx)+c(x); Theory

In this paper we develop a method to solve exactly partial differential equations of the type ( ⁿ /t ⁿ )f(x,t)=(a(x)( ⁿ /x ⁿ )+b(x) (/x+c(x))f(x,t); n=1,2, with several boundary conditions, where f·,t) lies in a function space. The most powerful tool here is the theory of cosine operator functions and their connection to (holomorphic) semigroups. The method is that generally we are able to unify and generalize many theorems concerning problems in the theories of holomorphic semigroups, cosine operator functions, and approximation theory, especially these dealing with approximation by projections. These applications will be found in [14].     

On polarized 3-folds (X, L) withg(L)=q(X)+1 andh 0(L)≥4

Let (X, L) be a polarized 3-fold over the complex number field. In [Fk3], we proved thatg(L)≥q(X) ifh ⁰(L)≥2 and moreover we classified (X, L) withh ⁰(L)≥3 andg(L)=q(X), whereg(L) is the sectional genus of (X, L) andq(X)=dimH ¹(O _X ) the irregularity ofX. In this paper we will classify polarized 3-folds (X, L) withh ⁰(L)≥4 andg(L)=q(X)+1 by the method of [Fk3].