椭圆性

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。

It s difficult to discuss the existence of nontrivial solution for an elliptic equation involving critical exponent.

利用集中紧引理和Hardy不等式克服这个困难，运用山路引理证明了一类非线性椭圆方程非平凡解的存在性

In this paper, reconstruction is provided for two convection coefficients or corresponding nonlinear term from Dirichlet to Neumann map determined by the boundary measurements of the solution of the elliptic equation in the plane.

本文提供了由平面椭圆型方程解的边界性态所确定的Dirichlet-Neumann映射求解方程两个对流系数或相应的非线性项的方法。

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。

He proved that the existence of the quasi-periodic solutions when the toriadmit 2-dimensional elliptic equilibrium point.

他证明了当系统有二维椭圆不动点时拟周期解的存在性。

The existence of weak solution for quasilinear elliptic system in the whole space is studied.

讨论了在全空间上拟线性椭圆型方程组的非平凡解的存在性。

The last part four, we discuss the exsitence and nonexistence of positive solution to a semilinear elliptic system.

论文的最后一部分是讨论椭圆方程组正解的存在性问题。

After that the existence of a nontrival solution for the elliptic system is proved by means of Mountain-Pass Lemma. At last, we present two examples to illustrate that our condition is weaker than Boccardo and De.

Figueiredo(2002)的条件更弱的条件下满足条件，并利用山路引理证明了这类拟线性椭圆型方程组非平凡解的存在性，最后举出两个例子验证了文中所给条件的确比Boccardo和De。

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

Using the method of blow up lower and upper solutions, the existence and boundary behavior of positive boundary blow up solutions for some elliptic systems of competitive type with singular weight functions are obtained, here the singular weight functions are permitted to be bounded in some parts of the boundary, and to go to infinity or even oscillate in other parts.

利用爆破上、下解方法，本文建立了带奇异权函数的竞争型椭圆方程组正的边界爆破解的存在性和边界行为，这里奇异权函数可以在边界的某一部分有界，而在其他的部分趋于无穷或者震荡。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。