解空间

Concretely, firstly with Timoshenko beams, the fundamental formulae of solutions of dynamical equations, boundary conditions and initial conditions have been transformed by Laplace transformation. Secondly, in the Laplace regions , we gain the analytical solutions of impact forces at the impact contact points, shear and maximum inverse stress of beams. Then, by using Durbin numerical inverse method, we gain the numerical solutions of Timoshenko beams under various restriction conditions. Moreover, the graphs about impact forces at the impact contact points, shear and maximum inverse stress of beams can be obtained too.

把Timoshenko梁力学模型动力学方程的基本解形式、边界条件以及初始条件进行Laplace变换，在Laplace区域得到了冲击接触处的冲击力、整个梁的最大弯曲应力和剪力的解析解，然后利用Durbin数值反演的方法得到了各种约束条件下的Timoshenko梁模型时间-空间的数值解，得到了冲击接触处的冲击力、梁各处的最大弯曲应力和剪力的曲线图。

Furthermore,under some assumptions,the relationship was also established between the global solutions of the augmented Lagrangian function on some c...

进一步地，在对全局解的一定假设下，还提供了原约束问题的全局最优解与增广Lagrange函数，在原问题变量空间的一个紧子集上的全局最优解之间的一些对应关系。

Using the method of dividing variables , the solution of elastic dynamics can be changed into the eigen value problem of Hamilton s space differential operator matrix , and the total solution of dual variable s (modal strain and modal strain rate ) can be obtained by .

采用分离变量方法，将弹性动力学解转变为Hamilton空间算子矩阵的本征值问题，对偶变量的全解通过本征解来展开而获得。

Since the solutions of this problem are the critical points of the associated energy function. One generally needs some compactness such as PScondition or C-condition to prove the existence of critical points of the energy func-tion, but when we study the elliptic equation in R~N, the compactness condition does not always hold since the imbedding of the Sobolev space H_0~(1,2)into L~(2*) is not compact. In this chapter, based on the nonsmooth critical point theory, and by using the approximation technique with periodic function, the existence of nontrivial solution is obtained.

由于该方程的解就是其所对应的能量泛函的临界点，通常都要在一些紧型条件的基础上来证明其所对应的能量泛函临界点的存在性，但当我们在无界域上考虑该椭圆方程解的存在性时，Sobolev空间H_0~(1，2)到L~(2*)的嵌入非紧，从而导致所对应的能量泛函失去紧性，本章在非光滑临界点理论的基础上，应用周期逼近的方法证明该问题非平凡解的存在性。

In this thesis, the barotropic primitive equation under the rectangular coordinate system and atmospheric circulation equation under p coordinate system are.

从正压原始方程开始，运用分层理论研究大气环流方程组定解问题的适定性，以及适定的定解问题(包括初值问题、边值问题和混合问题)在解析函数类空间准确解的求解方法。

Based on stratification theory, begin with the barotropic primitive equation, some theoretical problems of atmospheric equations are discussed, including the well posedness of their initial value problem, boundary value problem and mixed problem.

摘要从正压原始方程开始，运用分层理论研究大气环流方程组定解问题的适定性，以及适定的定解问题(包括初值问题、边值问题和混合问题)在解析函数类空间准确解的求解方法。

To a general KdV equation with singular curves on phase plane, we explain the reason why these non-smooth traveling wave solutions arise.Based on the bifurcation analysis, all possible traveling wave solutions have been known qualitatively.

论文的第三章考虑奇异性对非线性波动方程解的结构的影响，针对相空间上出现奇异线的广义KdV方程，详细讨论了奇异线的存在对解的结构的影响，分析系统中非光滑行波解产生的原因。

In this paper, a series of strong convergence theorems are discussed, which concern with generarized set-valued variational inclusions, a class of strongly accretive operator equation and a class of nonexpansive mappings.

第二章，我们在Hilbert空间中研究-单调算子的概念，以及与此相关的预解式算子R_~，利用预解式算子技巧构造了一类迭代算法，求解变分包含的逼近解问题，并讨论了由此算法产生的迭代序列的收敛性。

By using the cone theory and the coupling upper and lower solution method, it is studied the existence uniqueness of solutions of nonlinear binary operator equations without monotone and continuity and compactness conditionsin Banach spaces.

利用锥和耦合上下解方法，研究Banach空间不具有单调性、连续性和紧性条件的非线性二元算子方程解的存在唯一性，并给出了迭代序列收敛於解的误差估计，所得结果改进和推广了混合单调算子方程的某些已知相应结果。

By using the cone theory and the coupling upper and lower solution method,it is studied the existence uniqueness of solutions of nonlinear binary operator equations without monotone and continuity and compactness conditionsin Banach spaces.

利用锥和耦合上下解方法，研究Banach空间不具有单调性、连续性和紧性条件的非线性二元算子方程解的存在唯一性，并给出了迭代序列收敛于解的误差估计，所得结果改进和推广了混合单调算子方程的某些已知相应结果。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失