As the foundation of his first-order partial differential equation theory,Lagrange s definition plays an important role in his general integral theory.
从微观角度看,拉格朗日基于欧拉的定义,在用"常数变易法"探讨一阶偏微分方程积分的过程中受到启发,萌生了其积分"完全性"的新思想,并把这种新思想运用于常微分方程的研究,成功解释了奇解,在此基础上提出了一阶偏微分方程完全积分的新定义,因此拉格朗日完全积分的新定义是"常数变易法"和微分方程奇解现象共同诱发的产物。
We proper the existence of global smooth solution on Ω={-∞,<x<+∞,t≥0} for the generralized Cauchy problem of first order quasilinear P.
本文研究了下列一阶拟线性偏微分方程的广义Ｃａｕｃｈｙ问题：ｕｔ＋λ（ｕ）ｕｘ＝０，ｕ｜Γ＝φ（ｘ），Γ：ｘ＝ｒ（σ），ｔ＝ｓ（σ）。
This paper studies oscillation for the solutions of neutral higher order partial differential equation with continuous distributed deviating arguments.
研究了一类含有连续分布滞量的中立型高阶偏微分方程解的振动性,获得了该方程在两类边值条件下解振动的充分条件。
An impulse noise removal algorithm by detection technology and fourth-order PDE
一种结合检测技术与四阶偏微分方程的去噪算法
Reserches on the Value Distribution Theory and the Solutions of Systems of Higher-order Partial Differential Equations;
值分布理论及高阶偏微分方程组解的研究
Asymptotic Behavior for a Class of Higher-order Delay Partial Differential Equations;
一类高阶时滞偏微分方程的解的渐近性(英文)
Oscillation for Solutions of Certain Higher Order Neutral Partial Functional Differential Equations;
一类高阶中立型偏泛函微分方程解的振动性
Existence of Periodic Solutions for Higher Order Functional Differential Equation with Deviating Arguments
具偏差变元高阶中立型微分方程的周期解
Some Boundary Value Problems for High-order Complex Equation and Partial Differential Equations in Higher Dimensional Domains
高阶复方程和高维区域上偏微分方程的某些边值问题
Fractional Partial Differential Equation s Numerical Solution and Fundamental Solution;
分数阶偏微分方程的数值解及基本解
Theoretical and Numerical Investigation of Fractional Partial Differential Equations
分数阶偏微分方程的理论和数值研究
Bernstein Property of Solution to a Class Forth Order PDE;
一类四阶偏微分方程解的Bernstein性质
Domain Wall Waves of the Cubic Nonlinear Equation;
一个三阶非线性偏微分方程的域墙波
A Class of Problem for Determining Solution of Second-order Linear Partial Differential Equations of the Solution of the Problem
一类二阶线性偏微分方程的定解问题
Existence of Periodic Solutions for a Class of High Order Functional Differential Equations with Partial Difference Variables
一类具有偏差变元的高阶泛函微分方程周期解的存在性
Oscillation of Solutions to Higher-order Nonlinear Differential Equations of the Neutral Type
一类高阶非线性中立型偏微分方程系统解的振动性
The EXISTENCE OF PERIODIC SOLUTIONS FOR A KIND OF HIGH-ORDER FUNCTIONAL DIFFERENTIAL EQUATION
具偏差变元的高阶泛函微分方程的周期解存在性问题
Reducing a Second Order Differential Equation to a Higher Equation with Constant Coefficients;
化二阶微分方程为高阶常系数微分方程
Asymptotic Behavior of Solutions of Certain Higher Differential Equations and Higher Difference Equations;
一类高阶微分方程及高阶差分方程解的渐近性
Texture preserving fourth order PDE-based image denoising
具有纹理保持能力的四阶偏微分方程去噪方法
The Extent of Comparison Theorems of Ordinary Differential Equations to the Higher Order;
一阶常微分方程比较定理的高阶推广
Some Second Order Elliptic Partial Differential Equations on Unbounded Domain;
某些无界区域上的二阶椭圆型偏微分方程