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We study the existence of nonlinear elliptic equation by variational method and critical point theory, combined with sub- and sup-solution method.

第二章我们考虑非线性椭圆方程和带有局部p-凹凸非线性项的p-Laplace方程解的存在性，其中λ是正参数，0＜p＜1＜q。

Keywords: meshless method;adaptive algorithm;elliptic equation; variational inequality.

中文关键词：无网格方法；自适应算法；椭圆型方程；变分不等式

In this paper, a semilinear elliptic equation with critical Sobolev-Hardy exponents is studied, the existence of nontrival solutions for which is proved by the linking theorem in variational calculus.

该文研究了一类带有Sobolev-Hardy临界指数的半线性椭圆方程，运用变分理论中的环绕定理证明了方程非平凡解的存在性。

The metric variational energy momentum tensor and the Belinfante tensor is equivalent and gauge invariant.

如果经典的作用量在度规的表达变换下不变，那么能动张量的迹为零， g^{ab}T_{ab}=0

It also researches the application of variational method to solve the perturbation function in the energy principle.

本文还探讨了变分方法在求解能量原理中的扰动函数的应用。

For one-dimensional ocean temperature model, we optimally determined the initial and boundary conditions and related model parameters through variational assimilation method along with inverse problem techniques using incomplete and complete observational data,so as to determine the variation of position of epilimnion which has influences on SST.

由于温跃层的变化对海表温度的影响，我们以简单的海温模式为例，采用变分同化技术及反问题的技巧，在局部和整体观测资料下，对初、边值条件和模式参数等进行最优估计，确定温跃层的位置及其变化规律。4。

Then we derive first-order necessary optimality conditions for optimization problems with affine variational inequality, which joint upper-level feasible region Z includes a linear inequality constraint and a linear equality constraint.

其次，我们研究Luo的带仿射变分不等式约束优化问题，其中上水平约束Z不仅含有线性不等式约束，而且含有等式约束情形时的一阶最优性条件，同时还给出了Z的切线锥的表达式。

The solution of the linear variational inequality problem is transmuted to an equilibrium point of neural networks.

线性变分不等式问题的解被转化为神经网络的平衡点。

In the paper, we use the same idea to solve the variational equation,which equivalent to the Fredholm integral equation of the first kind with constraint.

这个积分方程的解只能确定到相差一个与边界的法向量成比例的向量，且在边界上的积分必须为零。

Variational regularity of the normalized equivalent radius( r norm= r/Λ) with normalized frequency is found out for different photonic crystal fiber parameters.

该分析和结果可为利用有效折射率法分析光子晶体光纤时等效芯半径的选取提供一定的理论依据。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。