In the linear integral equation φ(x)=f(x)+λ∫b ak(x,t)φ(t)dt,when the scope of λ extends from λ<1 (b-a)maxx,tk(x,t) into λ<1maxx ∫b ak(x,t)dt, the above equation also has its only solution.
线性积分方程 φ(x) =f(x) +λ∫bak(x ,t) φ(t)dt中 ,λ的取值范围由 λ <1(b -a)maxx ,t k(x ,t) 拓广为λ <1maxx ∫ba k(x ,t)dt时仍有唯一解。
The linear integral equation φ(x)=f(x)+λ∫b ak(x,t)φ(t)dt has its unique solution after the extension of the scope of parameter λ,and if separate the function k(x,t)into the products of function H(x) and G(t),the general solution form of the equation is φ(x)=f(x)+αH(x),(α is a constant).
拓广线性积分方程φ(x)=f(x)+λ∫bak(x,t)φ(t)dt中参数λ的取值后,方程仍有唯一解,且当k(x,t)可以分离为两函数H(x)与G(t)之积时,该方程解的一般形式为:φ(x)=f(x)+aH(x)(α为常数)。
As an application,we utilize this result to study the existence problem of solutions for some kind of nonlinear integral equations.
得出了一个新的不动点定理,推广了Alt man不动点定理,并利用这一新的不动点定理研究了一类非线性积分方程解的存在性问题。
This paper deals with the problem for solving a class of nonlinear integral equations in reproducing kernel space W(Ω) .
本文在再生核空间中,利用再生核把非线性积分方程化为线性积分方程,研究了此类方程的求解问题,揭示了此类方程解的结构,存在性及多解等问题。
The authors study the prob1em for so1ving a c1ass nonlinear integral equation in the reproducing kernel space W_2~1[a, b].
在再生核空间中，利用再生核方法，把一维非线性积分方程K_1uＫ_2u＝f转化为二维线性算子方程Ｋｕ＝ｆ。
Furthermore, we utilize our results to study the non zero solution and positive solution and properties of the solution for a class of the nonlinear integral equations, and some new results are obtained.
得到凝聚映象的几个新的不动点定理 ,并用到一类非线性积分方程的非零解、正解和解的性状的研究上得出了新的结果 。
linear integral equation of the third kind
第三种线性积分方程
The Existence of Continuous Solutions on a Nonlinear Integral Equation;
一类非线性积分方程连续解的存在性
Concise Solution of Linear Integral Equation after Extending the Scope of Parameter
拓广参数值后线性积分方程简明解法
Existence and Uniqueness of Positive Solutions for Some Nonlinear Integral Equations
一类非线性积分方程的正解存在唯一性分析
nonlinear integro-differential equation
非线性积分微分方程
Solutions to Several Classes of Nonlinear Differential Equations and Integral Equations;
几类非线性微分方程和积分方程的解
Asymptotic Behavior of Solutions of Certain Second Order Integro-differential Equations;
二阶非线性积分-微分方程解的有界性
Solvability of Systems of Nonlinear Hammerstein Integral Equations;
非线性Hammerstein积分方程组的可解性
The Integrability of the n-order Variable Coefficients Linear Ordinary Differential Equation
n阶变系数线性常微分方程的可积性
The Solution of n step even Linear Differential Equation that is a kind of can Change into Successive integral;
逐次积分法解一类齐次线性微分方程
Research on Some Problems of Nonlinear Integro-Differential Equations
非线性积分微分方程若干问题的研究
Stability Analysis of One-Leg Methods for Nonlinear Integro-Differential Equations
非线性积分微分方程单支方法的稳定性分析
The Regularizing Solution of Nonlinear Abelian IntegralEquation
非线性阿贝耳积分方程的正则化求解
Integrability Conditions of A Class of Third-order Nonlinear Differential Equation;
一类三阶非线性微分方程的可积条件
Solution of kind of second-order variable coefficient differential equation;
几类二阶非线性微分方程的可积类型
Integral Criteria of One Kind of First-order Nonlinear Differantial Equation;
一类一阶非线性微分方程的可积判据
Integral Criterion of One Kind of New Nonlinear Differential Equation;
一类新非线性常微分方程的可积判据
Solve the Nonlinear Schrodinger Equation by the Precise Integration Method
用精细积分法求解非线性薛定谔方程