查询词典 nontrivial solution

He existence and stability of the nontrivial and nonnegative steady-state solution of an ecological predator-prey system with the reaction-diffusion term are discussed.

应用渐近展开的方法构造生物学里提出的一类具有反应扩散项的捕食者─食饵系统的非平凡非负定态解，并应用固有值的解析摄动理论对所获得的非平凡非负定态解进行了稳定性分析。

The paper deals with the existence of nontrivial solution s to a class of nonlinear Hammerstein eigenvalue problems using the cone theory and the topological approach.

运用锥理论和拓扑方法研究一类非线性Hammerstein本征值问题的非平凡解。最后，把抽象结果应用于研究Lidstone本征值问题的非平凡的存在性

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。

The birth rate of the population is assumed to be a bifurcation parameter and nontrivial nonnegative steady-state solution bifurcated from the trivial steady-state solution has been obtained with the bifurcation theory.

应用分歧理论讨论一类单种群模型的非负定态解，并对该解的稳定性进行了分析。

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。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失