With the aid of eigenvalue, the P-stability of some non-trivial solutions of the mathematical model is achieved.
借助特征值法，研究相应弹性变形非平凡解的P-稳定性。
An improved GA was presented for finding several representative and satisfactory solutions of a category of multi-objective systems uniformly distributed on the set of non-trivial solutions.
为求得一类多目标系统在有效解集上均匀分布的多个具有代表性的满意解，提出一种改进的GA算法。
The result leads to the permanence of the prey-predator systems, the instability of the trivial and all forms of semitrivial solutions, and the nonexistence of nonuniform steady-state solutions.
这个结果导致捕食食饵系统的持久性、平凡解和所有半平凡解的不稳定性和不存在非一致平衡解。
Lyapunov's functions of a type of nonlinear third-order systems are constituted in this paper, and sufficient conditions assuring the global asymptotic stability of the trivial solutions are given.
在本文中，构造出了一类三阶非线性系统李雅普·诺夫函数，并给出这些系统全局渐近稳定的充分条件。
Mapping XML data to the relational model is not a trivial task (maybe one of the reasons for the variety of mapping solutions in the market).
将XML数据映射到关系模型不是一件普通的任务(这也许就是市场上存在多种映射解决方案的原因之一)。
By establishing a prior inequality, we prove that, under suitable conditions, the unique non-negative solutions of the problems are trivial.
在适当的条件下，通过建立一个先验不等式，证明了其唯一非负解是平凡的。
The global existence-uniqueness of solutions is obtained and the easy verifiable sufficient conditions for local asymptotic stability of a non-trivial steady-state solutions are given.
获得了解的整体存在惟一性，并给出了非平凡平衡解局部渐近稳定性易验证的充分条件。
Among the various approaches, the Darboux transformation is a very powerful tool for constructing soliton solutions of the NLEEs from a trivial seed.
其中达布变换是一种十分有效的方法，它能够从孤子方程的一个平凡解出发求出一系列孤子解。
Among the various approaches, the Darboux transformation is a very powerful tool for constructing soliton solutions of the NLEEs from a trivial seed.
其中达布变换是一种十分有效的方法，它能够从孤子方程的一个平凡解出发求出一系列孤子解。
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