平凡

Finally, natural frequency is obtained by the existence condition of nontrivial solution of the numerically discrete algebraic equations derived from the integral equations.

最后由积分方程的离散化方程组有非平凡解的条件，求得固有频率。

Under some conditions we obtain the existence of nontrivial solution by analyzing the best Sobolev embedding constant and by use of the minimax theorems without conditions.

通过使用没有条件的极小极大定理，以及对最佳Sobolev嵌入常数的详细分析，得到了一些具临界Sobolev指数的半线性椭圆系统的真正非平凡解的存在性，并讨论了解的一些性质。

Later, we estimate our variational functional to get a nontrivial solution of the new equation and so the second solution for is obtained.

然后我们利用函数平移将原来的非齐次边界问题转化为奇次边界问题，验证了其对应的变分泛函满足不带条件的山路引理的两个条件，并给出了泛函临界点存在的一个充分条件，最后对具体的变分泛函进行估计，得到了新方程非平凡解的存在性结果，从而得到了原方程第二个正解的存在性结果。

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。

Though, normality is kind of happiness.

但最终，我还是甘於平凡的。

You will really appreciate all the normality and depression when there comes success.

当你成功了，你会感谢曾经的沮丧和平凡。

I was born in Northern China.

我是一个平凡善良的人。

Some nouveau riche want to eat what ordinary people can't eat in order to show off their wealth.

一些暴发户想要吃平凡人吃不到的东西，以炫耀自己很有钱。

I always been thinking of that if he born nowaday, he should have had a different beautiful life...

我常想着，如果他在这个年代出生，，那么他会是一个不平凡的人，他会有一个不同的美好人生。

Mr O'Rourke, 65, a millionaire from business, real estate and insurance investments, chugs along as a conductor, earning a base salary of $52,000 a year.

65岁的奥卢克先生身为商业、地产和保险等投资业的百万富翁却宁愿做一个平凡的检票员，赚取微薄的5.2万美元的年薪。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。