查询词典 Moser

Firstly, the eigenvalue problem of a class of second order elliptic equation with critical potential and indefinite weights is considered. Then, using critical point theory, Trudinger-Moser inequality and the properties of the first eigenvalue, we prove the existence of a nontrivial solution for a class of nonlinear elliptic with critical potentialand indefinite weights in R~2. Secondly, we prove the existence of nontrivial solutions for a class of subcritical and critical elliptic systems with indefinite part in R~2 byusing a generalized linking theorem, Trudinger-Moser inequality and concentration-compactness principle.5. The existence of at least three weak solutions for discrete boundary value problem is established by using a three critical point theorem introduced by Ricceri.

首先，讨论了R~2中一类带不定权且含临界位势的二阶椭圆型方程的特征值问题，并借此特征值问题的第一特征值性质，利用山路引理及Trudinger-Moser不等式，证明了R~2中一类带不定权且含临界位势的非线性椭圆型方程非平凡解的存在性；其次，利用广义环绕定理，Trudinger-Moser不等式及集中列紧原理，得到了R~2上一类具有强不定部分的半线性椭圆型方程组在非线性项分别为次临界增长和临界增长情形下非平凡解的存在性。

Birkhoff, Siegel, Kolmogorov, Arnold, Moser, Herman, and many others investigated the ideas of stability and found complicated behavior for systems arising in celestial mechanics and other such physical systems, which could be described by what are called Hamiltonian differential equations .

Birkhoff ， Siegel ， Kolmogorov ， Arnold ， Moser ， Herman 和其他很多研究者研究稳定性的思想，发现了具有复杂行为的系统出现在天体力学和其它相似的物理系统中，这些都可以用称为 Hamilton 微分方程来描述。

Critical point theory;nonlinear elliptic differential and difference equation;existence of solution;multiply results;bifurcation;Trudinger—Moser inequality;applications

论文导师刘三阳，论文学位博士，论文专业应用数学论文单位西安电子科技大学，点击次数 4，论文页数 116页File Size3483K

The numercial simulation has been carried out, and the experimental results show that this method has been improved significantly comparing with the traditional one in nonlinear optics. Secondly, a second order system of semilinear elliptic equations, which comes from a mathematics model of the electric potential distribution of a media surrounded with the protein, is transformed into a variational problem, the existence of solution of it is proved by using variational principle and Trudinger—Moser inequality, and the relation between the solutions of variational problem and the solutions of its dual problem is obtained.

首先，讨论了非线性光学中的二次谐波产生的耦合方程组，利用变分法证明了耦合方程组非平凡解的存在性，然后进行了数值模拟，实验结果表明文中方法比经典的非线性光学中的方法有较大的改进，这对优化光倍频器件的设计将有所帮助；其次，将一类二阶半线性椭圆型方程组转化为一个变分问题，然后利用变分法和

Harald Moser of Rexam explained further: As consumers' lifestyles change, so do their needs and drinks packaging must meet these needs.

Rexam公司的Harald莫泽进一步解释说：随着消费者生活方式的改变，所以不要自己的需要和饮料包装必须满足这些需要。

Angelika Kauffmann and Mary Moser

安格莉卡。考夫曼和玛丽。

Here, we take the Moser iteration technique and study the two kinds of problems submitted above.

在本文中，我们利用Moser迭代的技术分别对两类问题进行了讨论。

Mr. Moser told us that his son had won the championship with a smile.

摩萨先生微笑着告诉我们，他的儿子获得冠军。

"It's been a possibility from the very beginning," Moser said.

"这事情基本上100％了"。

By Laura Moser Not long ago, I received an ominously official-looking correspondence from the ...

由劳拉莫泽不久前，我收到了不祥的官方的信件从。。。

"Yes, now you can give yourself airs," she said, you have got what you wanted.

"对了，您现在高兴了，"她说道，这是您所期待的。

Then the LORD said to me: Rebel Israel is inwardly more just than traitorous Judah.

上主于是对我说：＂失节的以色列比失信的犹大，更显得正义。