查询词典 consistent system of equations

Aim at the shortage of vertically additive method by which we can't discuss forced oscillations of systems of partial functional differential equations,we directly use the oscillatory definition,Green's formula and boundary condition of homogeneous Neumann to change the oscillatory problem of solutions to a class of systems of quasilinear parabolic equations of neutral type into the problem of which functional differential inequality haven't eventually positive solution.

针对垂直相加法无法讨论泛函偏微分方程组的强迫振动性的不足，直接利用振动的定义、Green公式以及齐次Neumann边界条件把中立型抛物微分方程组的振动问题转化为泛函微分不等式不存在最终正解的问题，然后利用最终正解的定义及上下极限得到了在齐次Neumann边界条件下判别其所有解振动或全振动的充分条件。

The difference equations and the perfectly matched layer absorbing boundary condition equations in the non-inertial frame are given.

将时域有限差分方法用于非惯性坐标系下光子晶体理论研究，给出了非惯性坐标系下的差分方程和理想匹配层边界条件。

Presents again a new formulation of Lagrange s equations by using an augmented Lagrangian function with the second order non linear nonholonomic constraint equations.

以Dirac方程为依据，求出了在电磁场作用下，质量为m ，自旋为 1 /2的荷电粒子在场中运动时的能量本征值及其拉氏函数密度的明显表示式，并对其微观物理机制作出了较为明晰的解

Presents a new formulation of Lagrange s equations by using an augmented Lagrangian function with the first order non linear nonholonomic constraint equations, and offers a unified variational approach to both holonomic and nonholonomic constraints.

采用带有二阶非线性非完整约束方程的扩张性拉氏函数，建立起了拉格朗日方程的又一新公式，该新公式较为规则，它提供了一种完整约束系统和非完整约束系统两者统一的变分方法。

And control problems such as optimal import rate control, optimal harvesting control, optimal birth control are investigated. By means of nonlinear functional analysis, differential equations, integral equations, and modern control theory, a number of research results are obtained, which are theoretically valuable and provide a solid ground for the practical use of our models.

本文系统讨论了几类年龄依赖的单种群和多种群动力系统，综合应用非线性泛函分析、微分方程、积分方程以及分布参数系统控制论等理论与方法，深入地研究了这些系统的解的存在性、唯一性以及非负有界性；研究了这些种群动力系统的最优输入率、收获率和出生率控制问题，获得了一批重要的理论成果。

In Chapter Ⅲ, by considering functions H k that may not have nonpositive partial derivative on s and employing integral averaging technique and Hardy inequality, the oscillation for a class of high order nonlinear differential equations and high order nonlinear damped differential equations is discussed, new oscillation criteria are established.

第二章利用广义Riccati技巧、积分平均技巧以及微分不等式理论，讨论了一类二阶非线性常微分方程的振动性，得到了若干新的振动准则，并讨论了该方程具有强迫项时解的渐近性态。

Finally, natural frequency is obtained by the existence condition of nontrivial solution of the numerically discrete algebraic equations derived from the integral equations.

最后由积分方程的离散化方程组有非平凡解的条件，求得固有频率。

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。

The existence of global weak solution for a class of generalized Ginzburg-Landau equations with an inhomogeneous boundary condition was studied. Some integral indentities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative and the square norm of partial derivatives were obtained.

研究具非线性边界条件的一类广义Ginzburg＿Landau方程解的整体存在性·推导了Ginzburg＿Landau方程的非齐次初边值问题光滑解的几个积分恒等式，由此得到了解的法向导数在边界上的平方模以及解的平方模和导数的平方模估计；通过逼近技巧、先验估计和取极限方法证明了Ginzburg＿Landau方程的非齐次初边值问题整体弱解的存在性

One of the primary methods to solve them is numerical method, and the other is Galerkin method, which change partial differential equations into normal differential equations, and then solve them with the traditional method.

小波分析已成为当前应用数学中迅速发展的新领域，它可以解决Fourier分析不能解决的许多困难问题，是近年来在研究工具及方法上的创新，已成为众多学科共同关注的热点。

There are different types of personal loans available.

有许多不同类型的个人贷款优惠。

The above mentioned teaching model of spiral rising can be used to avoid rigidness in teaching.

上述螺旋式上升的教学模式，可以避免教学形成模式後的僵化现象。