给出了一类全纯函数向量Riemann边值逆问题的一般提法.分齐次和非齐次两种情形,讨论了此边值逆问题正则型情况的可解性.利用全纯函数向量Riemann边值问题的有关理论,获得了该边值逆问题的可解条件和解的表示式.

In this paper,the general mathematical formulation of inverse Riemann boundary value problems of holomorphic function vector has been given,and the solvability of the homogeneous and nonhomoge-neous problem for the normal case has been discussed.On the basis of the theory of Riemann boundary value problems of holomorphic function vector,the solvable conditions and the representation of the solu-tions have been obtained.

给出解析函数的复合边值逆问题的数学提法.利用已有的复合边值问题的结果,讨论此边值逆问题的可解性,并给出其可解条件和解的积分表达式.

The mathematical formulation of inverse compound boundary value problem for analytic functions is given. Based on the theory of compound boundary value problem in plane,the solvability of the inverse compound boundary val-ue problem is discussed.The solvable conditions and the integral representations of the solutions are obtained.

研究非线性脉冲微分方程边值问题，应用分歧技巧，得到非线性脉冲微分方程边值问题多个解的存在性结果。

The nonlinear boundary value problem of impulsive differential equations is studied in this paper.By using bifurcation techniques we investigate the existence of multiple solutions for the nonlinear boundary value problem of impulsive differential equations.

研究了一类分数阶微分方程边值问题。应用Green函数，将分数阶微分方程边值问题转化为等价的积分方程，利用Schaefer不动点定理和Leray-Schauder不动点定理得到了该边值问题存在解的充分条件，推广和完善了已有的结果。

A class of boundary value problem of fractional differential equation is studied.By the means of the Green′s function, the boundary value problem of fractional differential equation can be reduced to the equivalent integral equa-tion, and some sufficient conditions on the existence of solution for the boundary value problem are obtained by using Schaefer′s fixed point theorem and Leray-Schauder fixed point theorem.Some known results are extended and im-proved.

研究了复合型第二种Weber方程的一类边值问题,经变量替换转换为变型的Hermite方程边值问题.通过引入左(右)相似核函数,得到边值问题的左区间解可由左区间相似核函数和左边界条件的系数进行组装,右区间解可由左边界条件的系数和左引解函数、交界面条件的系数和右相似核函数进行组装,证明了复合型第二种Weber方程组边值问题的解式具有相似结构,由此提出了求解该类边值问题的一个新解法——相似构造法.

A class of boundary value problem of the composite Second Weber system was investigated ,by us-ing the variable substitution ,the modified Hermite equations was obtained .By introducing left (right) similar kernel function ,the left interval solution of boundary value problem can be assembled by left similar kernel function and the coefficient of the left boundary condition ,the right interval solution of boundary value prob-lem can be assembled by right similar kernel function and the coefficient of the left boundary condition ,func-tion of left guide solution and the coefficient of interface conditions ,it is proved that the solution of boundary value problem of the composite second Weber system has the similar structure .And a new method is obtained for solving the composite boundary value problem ———similar constructing method (shortened as SCM ) .