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By use of the stretch and compression fixed point theorem of normic form in cone ,the sufficient conditions for the existence of monotone increasing positive solutions and monotone decreasing negative solutions are obtained to the boundary value problems.

运用锥拉伸与锥压缩不动点定理，分别得到了边值问题单调递增正解和单调递减负解存在的充分条件。

Delay differential equations; variational structure; Minimax theory; Morse theory; multiple periodic solutions; subharmonic solutions; Z_p geometrical index

基础科学，数学，数学分析时滞微分方程；变分结构；极小极大理论； Morse理论；多重周期解；次调和解；广义Z_p几何指标

In this paper, using Moser Twist Theorem, we obtain the existence of quasi-periodic solutions and the boundedness of solutions for Duffing equations and Liénard equation with some symmetric structure.

本文将利用Moser的扭转定理来研究Duffing方程和具有某种对称性的Liénard方程的拟周期解的存在性以及解的有界性。

Are also given by constructing Lyapunov function. Finally, by applying the energy methods, Sobolev embedding theorems and bootstrap arguments, the global existence of nonnegative classical solutions to equations with homogeneous Neumann boundary value condition is proved when the space dimension is at most 5. Under certain conditions for the coefficients of the reaction functions, the convergence of the solutions is established for the system with large diffusion coefficients by constructing Lyapunov function.

的正平衡点全局渐近稳定的充分条件；最后，当空间维数不超过5时，应用能量估计、Sobolev嵌入定理和bootstrap技巧证明在齐次Neumann边值条件下非负古典解的整体存在性，并通过构造Lyapunov函数给出当反应函数的系数满足一定条件、扩散系数较大时该模型解的收敛性。

Firstly, the eigenvalue problem of a class of second order elliptic equation with critical potential and indefinite weights is considered. Then, using critical point theory, Trudinger-Moser inequality and the properties of the first eigenvalue, we prove the existence of a nontrivial solution for a class of nonlinear elliptic with critical potentialand indefinite weights in R~2. Secondly, we prove the existence of nontrivial solutions for a class of subcritical and critical elliptic systems with indefinite part in R~2 byusing a generalized linking theorem, Trudinger-Moser inequality and concentration-compactness principle.5. The existence of at least three weak solutions for discrete boundary value problem is established by using a three critical point theorem introduced by Ricceri.

首先，讨论了R~2中一类带不定权且含临界位势的二阶椭圆型方程的特征值问题，并借此特征值问题的第一特征值性质，利用山路引理及Trudinger-Moser不等式，证明了R~2中一类带不定权且含临界位势的非线性椭圆型方程非平凡解的存在性；其次，利用广义环绕定理，Trudinger-Moser不等式及集中列紧原理，得到了R~2上一类具有强不定部分的半线性椭圆型方程组在非线性项分别为次临界增长和临界增长情形下非平凡解的存在性。

By using the method of upper and lower solutions ,we obtain the existence of solutions for boundary value problem of second order integro differential equations of Volterra type in a normal cone.

利用上、下解法在正规锥上证明了二阶非线性Volterra型积分微分方程边值问题解的存在性。

In order to achieve accurate solutions of ill-conditioned GPS equations with a few observational epochs, the ill-conditioned normal equations of GPS rapid positioning was transformed as a function optimization problem. Then genetic algorithm was used to calculate parameter solutions, which avoided the inversion of coefficient matrix of normal equations.

为准确解算仅有少数几个历元的GPS载波相位观测数据的病态定位方程，将GPS快速定位的病态法方程求解问题转化为一个函数优化问题，应用遗传算法求解病态方程，避免了法方程的求逆运算，从而可以得到参数的近似最优解。

The uniform of nonlinear incremental equation at critical points or non-critical points are deduced, and the relations between incremental solutions and nullspace basis of incremental matrix are put forward. So the incremental solutions can be obtained directly by nullspace basis, and can be expressed nullspace basis of matrix.

推导了非线性增量平衡方程在极值临界点与非临界点解的统一形式，指出增量解与增广矩阵零空间基的关系，从而可直接由零空间基获得增量解，并直接表示为增广矩阵零空间基的形式。

The responses of mature and immature adults of Bactrocera correcta to methyl eugenol solutions at different concentrations (1%, 3%, 5%, 7%, 9%, w/w), to the mixture of ME and a sweet bait VA (12.5% vinegar, 25% alcohol and 62.5% H2O), and to the combination of the volatiles of ME solutions at different concentrations and a sweet bait SVA (2.5% sugar, 12.5% vinegar, 25% alcohol and 60% H2O) odor, were tested in Y-tube olfactometer in laboratory.

利用 Y-嗅觉仪测试不同生理状态番石榴实蝇 Bactrocera correcta两性成虫对系列质量分数(1%， 3%， 5%， 7%， 9% w/w)甲基丁香酚溶液、系列质量分数ME溶液与醋酒溶液醋∶酒∶水＝12.5%∶25%∶62.5%(w/w， VA混合液、系列质量分数 ME挥发物与糖醋酒溶液糖∶醋∶酒∶水＝2.5%∶12.5%∶25%：60%(w/w， SVA气味混合物的反应。

Here mainly introduces five natures of the initial value problems, In several aspects summed up as the following : whether there are solutions to the problems, whether the only solution, the existence of solutions interval extent; Initial issues under what conditions have a solution--Cauchy - Piano existence theorem; how the district between the definition of a solution to open up a larger interval up; initial value problems for the sole condition --- Lipschitz conditions; 3、the numerical solution of the initial value problems of Ordinary Differential equations .

在这里主要介绍了初值问题的5个方面的性质，分别在这几个方面中总结了以下内容：初值问题是否有解，解是否惟1，解的存在区间有多大；初值问题在什么条件下有解----柯西-皮亚诺存在定理；怎样把在小区间上有定义的解开拓到较大的区间上去；初值问题解的惟1性条件---李普希茨条件；3：常微分方程初值问题的数值解法。

It has to be computed by the host for the actual clock rate.

主控制器可以用来计算实际的时钟速率。

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