non-tositif measurable function

The binary nonlinearization method is adopted to prove that there is an integrable decomposition of the Kaup-Newell equations in the sense of Liouville.

从2×2方阵形式的Kaup-Newell谱问题出发,构造了新的4×4方阵形式的Kaup-Newell谱问题,该谱问题的保谱发展方程族恰好是保谱Kaup-Newell方程的发展方程族;通过二元非线性化的方法,证明了4×4方阵形式的Kaup-Newell方程在刘维尔意义下存在一个可积分解。

The Integrable Condition for Riccati Equation;

关于Riccati方程的可积条件

A Type of Integrable Riccati′s Equation;

一类可积的Riccati方程

Studies an integrable question of Pfaff constraint,utilizing the integrable sufficient condition of Pfaff constraint,giving an integrable sufficient conditions of the Euler form as Pfaff constraint-proposition 1,and points out that the inverse-proposition of proposition 1 in general does not hold as proposition 2.

研究Pfaff约束可积性问题。

On integral criteria of some kinds of first-order differential equations;

再论几类一阶常微分方程的可积判据

By using the new comparis on function,more extensive asymptotic estimation formulas of the "intermediate point"in the first integral mean value theorem and the second integral mean value theorem are established under weaker conditions,which unify and extend corresponding results of[1-5][9-10].

引入比较函数概念,在g(x)可积的较弱条件下,建立了第一、二积分中值定理"中间点"更广泛的渐近估计式,作为推论又得到了微分中值定理和Taylor定理的"中间点"的渐近估计式,从而统一和发展了现有文献[1-5][9-10]中的最新结果。

Through the way of variable substitution,its integrable criterions and general integral are obtained.

给出几类非线性微分方程 ,通过变换来获得可积条件 ,同时给出它们积分的表达式 ,以达到拓宽其应用范围的目

A new result of integrability on the Abel equation;

关于Abel方程可积性的一个新结果

that a class of discontinuity points are distributed over limited smooth curves and that bounded bivar function in bounded closed region has the nature of integrability,by the use of the property that a smooth curve s area is zero.

本文主要通过光滑曲线面积为零的特性证明一类间断点只分布在有限条光滑曲线上并且在有界闭区域上有界的二元函数的可积性。

The paper is sufficient for first order nonlinear differential equation of the 1st kind y′=p(x)y+q(x)y~u+r(x)+ni=2f_i(x)y~i to be closed integrability.

给出了一类一阶非线性微分方程:y′=p(x)y+q(x)yμ+r(x)+n∑i=2fi(x)y′的较为广泛的一个封闭可积条件,该条件推广和统一了文献1中的定理1和定理2,特别指出近年来关于著名的Riccati方程和Abei方程可积性的一批最新结果都是它的特例。