一类二阶常微分方程m-点边值问题解的存在性  

The Existence of Solutions for a Class of Second-order m-point Boundary Value Problems

作　　者：魏小斐 曹文娟 WEI Xiao-fei;CAO Wen-juan(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院

出　　处：《数学的实践与认识》2019年第20期288-295,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11801243);甘肃省自然科学基金(1308RJZA113);兰州交通大学青年科学基金(2017012)

摘　　要：主要研究二阶常微分方程边值问题{y"(t)=f(t,y(t),y'(t)),t∈(a,b),y(a)=A,y(b)=αy(η),其中η∈(a,b)且α(η-a)≠b-a.非线性项f满足一定条件下,运用打靶法获得了该问题解的存在性,并将此结果推广到m-点边值问题.最后,通过MATLAB数值模拟验证了方法的可行性.In this paper,We mainly study three-point boundary value problem {y"(t)=f(t,y(t),y'(t)),t∈(a,b),y(a)=A,y(b)=αy(η),where η∈(a,b) and α(η-a)≠b-a.Under certain conditions of nonlinearity f,we obtained the existence by using the shooting method.Furthermore,we generalized this results to the m-point boundary value problem.Finally,we verified our result by MATLAB numerical simulation.

关 键 词：打靶法 存在性 M - 点边值问题 

分 类 号：O17[理学—数学]