摘要
为了研究具有完全形式的非线性四阶两点边值问题解的存在唯一性,考虑到非线性项函数中含有未知函数的所有低阶导数,在非线性项函数满足局部Lipschitz条件下,利用Green函数的性质以及压缩映射原理考察边值问题解的存在唯一性,并给出一致收敛于唯一解迭代序列的误差估计式;在非线性项函数依赖于未知函数及其二阶导数时,得到唯一解迭代序列相对于初始值函数的单调性。结果表明,采用压缩映射原理研究具有完全形式的四阶边值问题是可行、有效的。
To study the existence and uniqueness of the solution for a fully fourth-order two-point boundary value problem,considering that the nonlinear term contain all the low-order derivatives of the unknown function,the existence and uniqueness of the solution of the boundary value problem were investigated by using properties of Green＇s function and the principle of contraction mapping under the condition that the nonlinear term satisfied the local Lipschitz condition.The error estimate of the iterative sequences of approximations solutions was given. With the nonlinear term function depending on the unknown function and its second derivative,the monotonicity of the unique solution iteration sequence with respect to the initial value function was obtained. The results show that it is feasible and effective to study the fourthorder boundary value problem with complete form by using the principle of contraction mapping.
作者
马文杰
崔玉军
MA Wenjie;CUI Yujun(School of Mathematics and Systems Science,Shandong University of Science and Technology,Qingdao 266590,China)
出处
《济南大学学报（自然科学版）》
CAS
北大核心
2018年第4期344-348,共5页
Journal of University of Jinan(Science and Technology)
基金
国家自然科学基金项目(11371221
11571207)
山东省自然科学基金项目(ZR2018MA011)
关键词
边值问题
解的存在唯一性
压缩映射原理
迭代法
boundary value problem
existence and uniqueness of solution
contraction mapping principle
iterative method
