查询词典 nontrivial solution

Especially, we derive the Pohozaev identity for p-harmonic equation from which we obtain the corresponding nonexistence of nontrivial solution for p-harmonic equation with critical growth.

本文考虑了几类椭圆方程的Pohozaev恒等式，特别是对p-调和方程在两种边界条件下的恒等式作了详细的演算，并利用这些恒等式得到了一些解的非存在性结果。

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。

Based on chapter two, In chapter three, the method of multiple scales is introduced to the study of the multiple-dimensional nonlinear stochastic systems under random external excitation. Using method of multiple scales, we strictly deduce the equation of modulation of amplitude and phase. The effects of random excitations are analyzed; numerical simulations verify the results. Theoretical and numerical simulations show that when the intensity of the random excitation increases, the nontrivial steady state solution may be changed from a limit cycle to a diffused limit cycle.

在第二章基础上，第三章将多尺度法引入到相应的随机系统的研究中；严格推导了系统的约简方程，用矩方法求出稳态解应满足的方程，获得一些结果；并且数值模拟结果与理论推导的结果是一致的；并注意到，与其对应的确定性系统相比较，系统响应从周期解变为近似周期解，系统的相轨线从极限环变为扩大的近似极限环；随着激励带宽的增大，此扩大的近似极限环的宽度将增大。

Finally,for the n-unit ring network, by means of space decomposition,we establish sufficient conditions on the stability of the trivial solution and also consider the existence and stability of nontrivial equilibria.

最后，对n元环状神经网络系统，我们利用空间分解的方法讨论了平凡解稳定的充分条件以及该系统非零平衡解的存在性与稳定性。

In the final Chapter,we consider a system with cross-diffusion effects〓By using Liapunov-Schmidt method,the existence and stability of nontrivial sta-tionary bifurcation solutions from the trivial solution and the semitrivial stationarysolutions are studied.

在最后一章中，我们考虑一类含交叉扩散效应的方程〓3利用Liapunov-Schmidt分歧方法，我们研究了发自平凡定态解和半平凡定态解的非平凡定态分歧解的存在性和稳定性。

Secondly, by linearizing the system at the unique positive equilibrium solution and analyzing the associated characteristic equation, it is found that the positive equilibrium solution is asymptotically stable when the delay equals to zero and when it is increased to certain critical value, the positive equilibrium solution will loss the stability and a spatially heterohomogeneous periodic solution will bifurcate from this positive equilibrium solution.

通过在系统唯一的正平衡解处线性化系统和分析相应的特征方程，发现在时滞等于零时该正平衡解是渐近稳定的，当时滞逐渐增大到某个临界值时该正平衡解将失去稳定性而且在该平衡解处分支出空间非齐次的周期解。

Huang and Lin proposed the weak solution concept for Backward Stochastic Differential Equation This paper based on the predecessor's work , gives the weak solution concept for Backward Stochastic Differential Equation with continuous martingale,uses the Girsanov transformation, obtains its weak solution of the existence of a necessary and sufficient conditions, and on this basis obtains its weak solution of the existence of sufficient conditions,these sufficient conditions weakened the drifting coefficient which requested in the existence uniqueness of strong solution to satisfy the Lipschitz condition the request.

本文在前人研究的基础上，给出由连续鞅驱动的倒向随机微分方程弱解的概念，利用Girsanov变换，得到其弱解存在的存在的一个充分必要条件，并在此基础上得到了其弱解存在的一些充分条件，这些充分条件减弱了在强解的存在唯一性中要求的漂移系数满足Lipschitz条件的要求。

The invention discloses an InP quantum point preparing method, comprising the steps of:(1) mixing InCl3 with trioctylphosphine oxide, and preserving heat at 90-110DEG C to prepare a solution whose In content is 0.1-0.3mol/L;(2) raising temperature to 130-180DEG C, and charging argon gas;(3) injecting PSi(CH333 into InCl3-TOPO compound in the molar ratio of 1 to 1-1 to 2;(4) when the solution color turns into transparent red or orange, raising temperature to 260-270DEG C and preserving heat;(5) lowering temperature to 90-110DEG C and injecting dodecyl amine, decyl amine or mercaptan;(6) dissolving reacting mixture in nonpolar solvent to form transparent colloidal solution, then adding in polar solution until the colloidal solution is muddy, and centrifugally separating and obtaining deposits and supernatant; and (7) centrifugally separating the supernatant, where the above steps (1)-(5) are performed.

本发明公开了一种InP量子点的制备方法，其步骤为：①将InCl 3 与三辛基氧膦混合，在90～110℃保温制得In含量为0.1～0.3mol/L的溶液；②升温到130～180℃，通入氩气；③将PSi(CH 3 3 3 注射入InCl 3 -TOPO复合物中，其摩尔比为1∶1～1∶2；④待溶液颜色变为透明的红色或橙红色，将升温260～270℃保温；⑤降温到90～110℃，注入十二胺、癸胺或硫醇；⑥将反应混合物溶于非极性溶剂，形成透明的胶体溶液，然后加入极性溶剂，直至胶体溶液出现混浊状，然后离心分离获得沉积物和上层清液；⑦取上层清液进行离心分离。上述步骤①～⑤在保护气氛下进行。

Local lesion assay indicated that when mixed with TMV-infected leaf juice dilution within 3 minutes, 5 disinfectants showed 100% inactivation ratio, including 30% chloride of lime 1:9 solution, 98% trisodium phosphate 1:9 solution, 7% sodium hypochlorite 1:150 solution, anonymity disinfectant used in USA 1:125 solution, and 75% alcohol solution.

摘 要：为了指导烟草漂浮育苗中剪叶工具消毒剂的使用，采用半叶法测定了9种药剂对烟草病叶汁液中TMV的钝化效果，采用叶面喷雾法测定了药剂对烟草的药害浓度与药害症状。

The rheological character of a polymer often appears as shear-thinning. Most polymers behaviour in a solution can be explained by the polymer chain or hard sphere theory. Other than that, shear-thickening polymer solution also exists. Its behavior can be explained by dilatant theory, which suggests that the shear-thickening of the solution is due to the swelling of the polymer particles. This phenomenon often occurs in suspension or emulsion. Solution exhibits a mixed behavior can also be found whose behavior is such that shear-thinning occurs under low shear force and shear-thickening occurs under high shear force. Under this circumstance, the viscosity versus shear force graph exhibits a spoon shaped curve. The rheological study can be applied to the dispersion of paint which can predict the dispersion effect of various polymer materials in solution.

中文摘要一般高分子聚合物溶液的流变行为多半呈现剪稀(shear-thinning)的现象，而大部分的高分子在溶液中的行为是以分子链或是硬球观点来解释，另外也有剪稠(shear-thickening)现象的高分子溶液，其流变行为则是以膨胀体观点来解释，即在高剪切力下，由於高分子团体积变大而使溶液黏度升高，这在悬伏液、乳液等常见；但也有在低剪切力下，溶液具有剪稀的行为，而在高剪切力下却成现剪稠的行为，在黏度对剪切力作图时，会呈现出一个勾形曲线的图形；流变行为的探讨可应用在涂布材料的分散技术上，以推测不同的高分子溶液对分散效果的影响。

Now she was hungry and angry.She began to smoulder.

现在她又饿又气，她开始流露难以抑制的怒火。

You have placed our iniquities before You, Our secret sins in the light of Your presence.

诗90：8 你将我们的罪孽摆在你面前、将我们的隐恶摆在你面光之中。