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When this nonexistence need to express,then it becomes existence,but this nonexistence whether is another kind of existence?

当非存在需要表达，然后变成存在，但此非存在是否也是另一种形式的存在？

We will study the existence of sign-changing solution. In the second chapter, we consider the existence of sign-changing solutions for nonlinear operator equation and its application in abstract space.

尽管理论和应用中的许多问题均可归结常微分方程非局部问题，但由于非局部问题自身固有的难度，人们对非局部问题的研究起步相当晚。

It is chiefly in this sense that Berkeley denies matter; that is to say, he does not deny that the sense-data which we commonly take as signs of the existence of the table are really signs of the existence of something independent of us, but he does deny that this something is nonmental, that it is neither mind nor ideas entertained by some mind.

贝克莱主要是在这种意义上否定物质的；那就是说，他并不否认通常我们以为是桌子存在的标志的那些感觉材料是某种独立于我们之外的东西的存在标志，但是他确乎不认为这个某种东西可以是"非心灵"的，也就是说，可以既不是心灵，也不是某个心灵所具备的观念。

The main results and novelties of the paper are as follows:Firstly, we study the existence of nontrivial solution for the following nonlinear equations with singular pontential By using variational methods and critical point theory, we construct linking type critical value of this kind of singular elliptic equations, with the properties of the eigenvalue, we estimate the critical value and prove the local condition holds to show the existence of the nontrivial solution.

论文的创新点及主要结果如下：首先研究有界区域上具有奇异位势的非线性方程的非平凡解的存在性，运用变分方法与临界点理论，构造这一类奇异椭圆方程的环绕型临界值，并由特征值的性质给出临界值的估计，同时证明局部条件成立，最终证明方程非平凡解的存在性。

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。

These values are called existence vulnes which are subdivided into three categores: pure nonuse value、not repeatedly use valne and pure existence valne.

存在价值又分为纯不能利用的价值，不再利用的价值和纯存在价值三种。

Once you got a purpose in your mind, you obey the whole existence. When you focus on a purpose, you will meet frustration. When you obey the whole existence, you will not be succeed. You are the small one in the world.

一旦你有了一个目的，你就违反了整体——记住这一点——那么你就会有挫折，当你违反整体，你无法胜利。

In the wake of the above the classification, Rosenberge raised the principle for distribution of burden of proof: person who is in view of right existence is obligated to take the burden of proof according to the legal requirement for the right occurring; person who deny right existence is obligated to take the burden of proof according to the legal requirement for right obstacle, right nullification or right obviation.

在进行了上述法律规范分类后，罗森伯格提出的分配证明责任的原则是：主张权利存在的人，应就权利发生的法律要件事实负证明责任；否认权利存在的人，应对存在权利障碍要件，权利消灭要件或权利排除要件事实负证明责任。

According to Faraday's experiment, there must be a wire testing the existence of the electric field, just as there must be a magnetic pole, or needle, testing the existence of a magnetic field in Oersted's experiment.

根据法拉第的实验，必须有导线来检验电场是否存在，正像在奥斯特的实验中也必须有磁极或磁针来检验磁场是否存在一样。

The existence of a written contract depends on the fact that the offerer and offeree have interchanged their written expressions, not on the continued existence of those expressions.

书面合同的存在取决于要约人和受约人之间交流了书面表达之事实，而非那些表达的继续存在。

Methods Clinical data of 3 cases of bile duct injury during laparoscopic cholecystectomy were analyzed retrospectively.

回顾总结3例LC术中胆管损伤的临床资料，分析3例胆管损伤的原因及对策。

These techniques are applied to the gobang.

本文将这些技术用于五子棋中。