非齐次的

In chapter four,at first,we investigate classification theory of the positive homogeneous p-Laplacian equation ,the main method is Prufer's transformation,and then we discuss the nontrivial solution for associated nonhomogeneous equation by making use of Leray-Schauder degree.

接着研究了非齐次方程的可解性。在第四章中，我们首先是建立了正齐次p-Laplacian 方程的分类理论，主要利用Prufer 变换。再应用Leray-Schauder 度理论证明非齐次方程的可解性。

The second chapter is the main part of this paper, in which the formulation of the Riemann boundary value problem of non-normal type on the real axis, the solution method of homogeneous problem, the relation between the two kinds of different derivatives and the inhomogeneous problem will be thoroughly given. In this paper, the solution and the solvability of the Riemann boundary value problem of non-normal type on the real axis will be given. Furthermore, it is shown that the twokinds of derivatives of the function Ψ are existing and equivalent in the case ofthe solution about the original problem, therefore, we get uniformly Hermite interpolatory polynomial. The relation between the two kinds of different derivativesof the function Ψ are similar for smooth closed contours by means of the same proof.

第二章是本文的主要部分，分别给出了实轴上一类非正则型Riemann边值问题的提法、齐次问题的解法、两种导数的关系及非齐次问题的求解，本文运用杜金元教授[11]的方法获得了实轴上非正则型Riemann边值问题的封闭解及可解性条件，且在问题可解的情况下论证了函数Ψ的非切向极限导数和Peano导数存在且相等，从而获得了统一的Hermite插值多项式，同样关于封闭曲线上非正则型Riemann边值问题，采用本文论证方法证得了函数Ψ的非切向极限导数和Peano导数存在且相等，从而较好地统一了[10]、[11]中的Hermite插值多项式。

There is a relatively complete style of homogeneous function about the boundary condition in the problem of sure resolution of unhomogeneous boundary condition,which is based on the summarizing of mass former experiences and is proved in this article.

通过对非齐次边界条件的定解问题的讨论，引出了本文的论题，对非齐次边界条件定解问题的边界条件齐次化函数提出了一种比较一般和标准的形式，并提出了一个定理。对该定理进行了证明，证明了它的正确性。

In order to obtain more general solution of second order linear differential equation with constant coefficients, which is important in theory and practice, on the basis of knowing a special of the second order linear differential equation with constant coefficients and by using the method of variation of constant, the second order linear differential equation with constant coefficients is transferred to the reduced differential equation and a general formula of the second order linear differential equation with constant coefficients is derived.

为了更多地得到理论上和应用上占有重要地位的二阶常系数线性非齐次微分方程的通解，这里使用常数变易法，在先求得二阶常系数线性齐次微分方程一个特解的情况下，将二阶常系数线性非齐次微分方程转化为可降阶的微分方程，从而给出了一种运算量较小的二阶常系数线性非齐次微分方程通解的一般公式，并且将通解公式进行了推广，实例证明该方法是可行的。

The method is convenient to be used, especially to nonhomogeneous equations and nonhomogeneous boundary value problem.

用微分算子法给出了线性扩散方程和波动方程的通解及初值以及边值相关问题的算子解，特别是对非齐次方程和非齐次边界问题处理尤其简捷适用。

In the second part,we gave the theorem of inhomogeneous spectral inclusion regions of partitioned matrices,so some relevant researches have been improved in this field.

第二部分给出了分块矩阵的非齐次谱包含域定理。从而把有关矩阵非齐次谱包含域的研究工作做了一定改进。

Recently, Professor Liu Wen and his associates study the strong law of large numbers for Markov chain fields on trees. But for the nonhomogeneous Markov chain fields ,they only study the even-odd Markov chain and non-symmetric Markov chain. However, this article goes in the normal nonhono-geneous Markov chain fields and gets a class of limit theorems for the functions of two variables of finite nonhomogeneous Markov chain fields. Some limit theorems on the frequences of states and ordered state couples are obtained by several corollaries.

最近刘文教授及其合作者对树上的马氏链场的极限定理作了研究，对于非齐次马氏链场，仅对其中的奇偶马氏链场和非对称马氏链场作了研究，本文讨论了一般的非齐次马氏链场的极限性质，得到了关于Caylay树上有限非齐次马氏链场二元泛函的一类极限定理，作为推论得到了关于状态与状态序偶出现频率的极限定理。

In this project, we study the theory of higher order differential equations in Banach spaces and related topics. We solve an open problem put forward by two American Mathematicians and two Italian Mathematicians concerning wave equations with generalized Weztzell boundary conditions, introduce an existence family of operators from a Banach space $Y$ to $X$ for the Cauchy problem for higher order differential equations in a Banach space $X$, establish a sufficient and necessary condition ensuring $ACP_n$ possesses an exponentially bounded existence family, as well as some basic results in a quite general setting about the existence and continuous dependence on initial data of the solutions of $ACP_n$ and $IACP_n$. We set up quite a few multiplicative and additive perturbation theorems for existence families governing a wide class of higher order differential equations, regularized cosine operator families, regularized semigroups, and solution operators of Volterra integral equations, obtain classical and strict solutions having optimal regularity for the inhomogeneous nonautonomous heat equations with generalized Wentzell boundary conditions, gain novel existence and uniqueness theorems,which extend essentially the existing results, for mild and classical solutions of nonlocal Cauchy problems for semilinear evolution equations, present a new theorem with regard to the boundary feedback stabilization of a hybrid system composed of a viscoelastic thin plate with one part of its edge clamped and the rest-free part attached to a visocelastic rigid body. Also we obtain many other research results.

在本研究中，我们对Banach空间中的高阶算子微分方程的理论以及相关理论进行了深入研究，解决了由美国和意大利的四位数学家联合提出的一个关于广义Wentzell边界条件下的波动方程适定性的公开问题，恰当地定义了Banach空间中的高阶算子微分方程Cauchy问题的算子存在族及唯一族，建立了齐次和非齐次高阶算子微分方程Cauchy问题适定性的判别定理，获得了关于高阶退化算子微分方程的算子存在族、正则余弦算子族、正则算子半群、Volterra积分方程解算子族的乘积扰动和混合扰动定理，得到了关于以依赖于时间的二阶微分算子为系数的一大类非自治热方程非齐次情形下的时变广义Wentzell动力边值问题的古典解、严格解的最大正则性结果，获得了半线性发展方程非局部Cauchy问题广义解和经典解存在唯一的判别条件，从实质上推广了现有的相关结果；得到了一部分边缘固定而另一部分附在一粘弹性刚体上的薄板构成的混合粘弹性系统的边界反馈稳定化的新稳定化定理，还建立了一系列其他研究结果。

The former being solved by the boundary point methool,and the latter constructed by the analytic way,on natter whetter the problem is defined in finiter or infinite region,and steady or transient .

将微分方程的非齐次问题解化为相应齐次问题解与某个非齐次特解之和，前者用边界点法计算，后者则通过解析法来构造，无论是有限域或无限域、定常或非定常问题，本文方法都能得出可靠有效

In this paper, first, the unified form of W is presented on the condition of linear unhomogeneous boundary condition under stable condition.

从稳定条件下的线性非齐次边界条件出发，给出了w的统一形式，进而将其推广到非稳定条件下的非齐次边界条件，得到w的一般的结果。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。