四阶非线性常微分方程非线性三点边值问题解的存在性与唯一性  

Existence and Uniqueness of Solutions of Nonlinear Three-Point Boundary Value Problems for Fourth Order Nonlinear Ordinar y Differential Equations

作　　者：裴明鹤[1] 禹海兰[2] 

机构地区：[1]北华大学师范学院数学系,吉林市132013 [2]东北电力学院基础部,吉林市132012

出　　处：《数学物理学报（A辑）》2000年第2期194-201,共8页Acta Mathematica Scientia

摘　　要：该文利用“Matching”技巧 ,给出了四阶非线性常微分方程y(4) =f(x,y,y′,y″,y ) ,满足非线性三点边界条件k(y(b) ,y′(b) ,y″(b) ,y (b) ,y(a) ,y′(a) ,y″(a) ,y (a) ) =0 ,y(b) =μg(y′(b) ,y (b) ) =0 ,h(y(b) ,y′(b) ,y″(b) ,y (b) ,y(c) ,y′(c) ,y″(c) ,y (c) )In this paper,by using the “Matching” technique, gives concrete sufficient conditions of the existence and uniqueness of solution s of nonlinear three-point boundary value problems for fourth order nonlinear o rdinary differential equation\$\$y\+\{(4)\}=f(x,y,y′,y″,y),\$\$with the nonlinear three-point boundary c onditions\$\$k(y(b),y′(b),y″(b),y(b),y(a),y′(a),y″(a),y(a))=0, y(b)=μ, g(y′(b),y(b))=0, h(y(b),y′(b),y″(b),y(b),y(c),y′(c),y″(c),y(c))=0.

关 键 词：非线性常微分方程 三点边值问题 存在性 解 

分 类 号：O175.14[理学—数学]