反证法的

Under suit upper and lower solution, iteration sequences were constructed, and existence and unique of solutions of linear boundary value problems on second order nonlinear Hammerstein type integro-differential-difference equation were obtained by means of applying the Arzela-Ascoli theorem Lebesque control convergence theorem and disproof method.

在上下解存在的条件下，构造迭代序列，由Arzea-Ascoli定理和Lebesque控制收敛定理得到了二阶非线性Hammerstein型积分微分差分方程的线性边值问题的解的存在性。再利用反证法获得了解的唯一性。

Chapter 3 emphasizes on the case that the considered systems contain not only impulse but also time delay. We mainly investigate impulsive parabolic systems with time delay and neutral impulsive parabolic systems. Section 3.1 discusses the oscillation of impulsive parabolic systems with time delay under Robin boundary condition and obtains some useful criteria via first order impulsive differential inequalities with time delay. Section 3.2 studies the oscillation of neutral impulsive parabolic systems under Neumann boundary condition and Robin boundary condition, respectively, and obtains some sufficient conditions for oscillation and strong oscillation via first order neutral impulsive differential inequalities.

第三章针对于"脉冲"与"时滞"共存的复杂情形，仍采用反证法讨论了含时滞的脉冲偏微分系统的振动理论，具体研究了脉冲时滞抛物系统和中立型脉冲时滞抛物系统。3.1节考虑了脉冲时滞抛物系统的振动理论，借助于一阶脉冲时滞微分不等式的解的性质，得到了满足Robin边界条件的脉冲时滞抛物系统的若干振动准则；3.2节考虑了中立型脉冲时滞抛物系统的振动理论，借助于一阶中立型脉冲时滞微分不等式的解的性质，分别给出了满足Neumann边界条件和Robin边界条件的中立型脉冲时滞抛物系统的若干振动和强振动准则。

The key of our method is to reduce the exact controllability of a semilinear system to the observability estimate for the dual system of its linearized system.

另一方面，我们注意到，上述的两种方法无法给出任何能观性不等式中出现的常数的显式估计，因为它们采用的是反证法来吸收低阶项的。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。