有界型性

The purpose of this paper is to prove the existence of non-oscillatory solutions to second-order neutral time-lag differential equation with positive/negative coefficient by using contraction-image principle through defining an operator from a bounded,closed,and convex subset into Banach space.

通过定义有界闭凸子集到B anach空间上的一个算子，应用压缩映像原理讨论了带有正负系数的二阶中立型时滞微分方程非振动解的存在性，得到该方程非振动解存在的一个充分条件。

The first part presents develops of predator-prey systems and gives the model that is investigated in our paper; Chapter 2 presents the results on boundedness of solutions and permanence of system; In chapter 3, we explicitly derive a domain of attraction for the positive equilibrium of system by using Liapunov method; The local stability and the conditions that Hopf bifurcation occurs are obtained in chapter 4; In chapter 5, some explicit fomulae of the direction of Hopf bifurcation and the stability of bifurcating periodic solutions on the center manifold are determined,using normal form and center manifold introduced by Hassard et al; In chapter 6, some numerical simulations are performed to illustrate the analytical results found; Our paper ends with a brief conclusion.

全文共分七章，第1章对捕食-食饵系统的发展背景做了介绍并给出了本文研究的模型；第2章讨论了系统的保持性和解的有界性；第3章研究正平衡点的全局性质，对正平衡点的吸引域进行了精确估计；第4章研究了系统的正平衡点的局部稳定性和Hopf分支存在的条件；第5章利用规范型和中心流形定理得到了一个决定Hopf分支方向、分支周期解的稳定性及其他性质的精确公式；第6章对一个具体模型进行了数值模拟；第7章对全文进行了总结。

This paper makes use of a Lyapunov function and a nonlinear integral inequality of Gronwall-Bellman-Bihari type to study the asymptotic hehaviors of solutions of a second-order nonlinear functional differential equation.

本文利用李雅普诺夫函数及一个Gronwall—Bellman—Bihari型的非线性积分不等式，研究一类二阶非线性泛函微分方程解的渐近性态，在第一部份，给出一组方程的全体解可延展到t=+∞的充分条件及三组方程的全体解有界的充分条件。

This paper makes use of a Lyapunov function and a nonlinear integral inequality of Gronwall-Bellman-Bihari type to study the asymptotic hehaviors of solutions of a second-order nonlinear functional differential equation. In part I, a group of sufficient conditions is given on continuation of solutions and three groups of sufficient conditions are given on boundedness of solutuicns of equation.

本文利用李雅普诺夫函数及一个Gronwall—Bellman—Bihari型的非线性积分不等式，研究一类二阶非线性泛函微分方程解的渐近性态，在第一部份，给出一组方程的全体解可延展到t=+∞的充分条件及三组方程的全体解有界的充分条件。

Deviate argument; Limit circle case; Limit point case; The boundedness of solutions; Integral inequality

基础科学，数学，数学分析偏差变元；极限圆型；极限点型；有界性；积分不等式

The main results and novelties of the paper are as follows:Firstly, we study the existence of nontrivial solution for the following nonlinear equations with singular pontential By using variational methods and critical point theory, we construct linking type critical value of this kind of singular elliptic equations, with the properties of the eigenvalue, we estimate the critical value and prove the local condition holds to show the existence of the nontrivial solution.

论文的创新点及主要结果如下：首先研究有界区域上具有奇异位势的非线性方程的非平凡解的存在性，运用变分方法与临界点理论，构造这一类奇异椭圆方程的环绕型临界值，并由特征值的性质给出临界值的估计，同时证明局部条件成立，最终证明方程非平凡解的存在性。

Neutral equation; stochastic functional differential equation; stochastic differential equation with delay; infinite delay; asymptotic propertie; semimartingale convergence theorem; Markovian switching; moment stability; moment boundedness

基础科学，数学，概率论、数理统计中立型方程；随机泛函微分方程；随机延迟微分方程；无限时滞；渐近性质；半鞅收敛定理； Markov调制；矩稳定性；矩有界性

Along with the developing of the molecole characterization of the weighted Herz type Hardy space, the study of the singular integral operator get a plentiful harvest.

本文首先解决了加权Herz型Hardy空间的分子刻画，作为应用，给出了强奇异积分算子T_b在加权Herz型Hardy空间上的有界性的证明。

We also study the weighted composition operators between Hardy spaces on the unit ball, as well as between Bergman spaces. Some equivalent conditions that the operators are bounded or compact are given in term of the Carleson type measure.

另外，我们也考虑了单位球上Hardy空间之间及Bergman空间之间的加权复合算子，利用Carleson型测度，给出了有界和紧性的等价条件。

In Chapter 2, an existence theorem is obtained for periodic solutions of non-autonomous second order systems with even-typed potentials. We also investigate solutions of linear bounded positive self-conjugation operators equations in Hilbert Space by variation methods.

第二章主要利用临界点理论中的归药方法、极小作用原理研究具偶型位势的二阶非自治系统周期边值问题，得到了周期解的存在；利用变分方法证明了Hilbert空间中有界线性正自共轭算子方程解的存在性。

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。