查询词典 elliptic system

The aim of this paper is to study the existence of solution and multiply results for quasilinear elliptic system in bounded domain and the whole space, semilinear elliptic equation in two dimension space, second order nonlinear difference equation by variational methods. The main results are listed in the following:1. An abstract compactness theorem is proved, and then, under weak Boccardo and De.

本文主要利用变分法，分别研究了有界区域和全空间上拟线性椭圆型方程组、二维空间上半线性椭圆型方程和二阶非线性差分方程问题的解与多重解的存在性，具体内容如下： 1。

In this paper,at first we transformed the nonlinear elliptic system of 2m first order equations into the complex form, then by use the results on the Riemann-Hilbert problem for nonlinear elliptic complex equation of first order, the method of continuity, the Schauder fixed-point theorem and the Leray-Schauder theorem, we proved that the modified Riemann-Hilbert boundary value problem for the complex system with some conditions is solvable.

本文先将较一般的多个未知函数的一阶椭圆型实方程组化为复方程组，然后讨论这些复方程组在某些条件下的一些边值问题的可解性。这里所考虑的方程组既包含线性的，也包含非线性的，比广义超解析函数所满足的方程组还要广，又本文主要研究较一般的Riemann-Hilbert边值问题，先给出这种边值问题解的先验估计式，然后用参数开拓法及Leray-Schauder定理证明这种边值问题的可解性结果。

Second, we consider the strongly coupled elliptic system with homogeneous Dirichlet boundary conditions. The prior estimates for thesolution of nonlinear elliptic system are derived. It is shown that there is no coexistence state if diffusion rates are strong, or if the intrinsic growth rates are slow.

第二章研究带齐次Dirichlet边界条件的强耦合椭圆系统，首先推出非线性椭圆系统解的先验估计，然后证明了当食饵和捕食者的扩散率足够大，或者出生率足够小时，系统不存在共存现象，并给出半平凡解存在的充分条件。

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。

With the method of upper and lower solutions,its associated monotone iterations and the fixed point theorem,the coexistence solutions to a strongly coupled elliptic system are studied.

采用上下解及相应的单调迭代序列的方法，结合Schauder不动点定理，研究带Dirichlet边界条件的两种群的互惠模型强耦合问题共存解。

Because of the small-angle approximationof the parabolic system,we say the result of the elliptic system is relatively reliablein the interval of large ray angle.

由于抛物方程的小角度近似，我们认为在大掠射角区间内，椭圆方程的考察结果是比较可靠的。

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。

Since theparabolic system is an approximation from the elliptic system under small ray angle,we may have reasons to question the result of the parabolic system under large rayangle.

由于抛物方程是椭圆方程在小掠射角条件下的近似，我们有理由对抛物系统在大掠射角情况下的考察结果的可靠程度保持怀疑。

The Counihan system comprising of a castellated barrier wall, seven quart-elliptic vorticity generators and surface roughness was used to generate a deep, turbulent boundary layer.

Counihan系统的组成castellated屏障的墙，七quart-elliptic涡发生器和表面粗糙度是用来产生了深深的、湍流边界层的。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。