摘要
研究了一类四阶两点边值问题正解的存在唯一性。首先通过Laplace变换求出相应的Green函数G(t,s)并讨论了相关性质;然后,通过将方程右边简化为算子方程的方法,利用几个经典的不动点定理得到了该问题正解的存在唯一性;最后,给出了迭代方法和一个数值例子。本研究求解Green函数的方法更加直观易懂,且迭代方法更易实现。
In this paper,we studied the existence and uniqueness of positive solutions to a class of fourth-order two-point nonlinear boundary value problems.Firstly,by using the Laplace transform,we worked out the corresponding Green function and discussed some properties.Then,by reducing the boundary value problem to operator equation for right-hand side function and using some classical fixed point theorems,we obtained the results about the existence and uniqueness of the positive solution.Finally,we gave an iterative method and a numerical example.The proposed method of solving Green function is more intuitive and easier to understand,and the iterative method is easier to implement.
作者
韦孝东
白占兵
WEI Xiaodong;BAI Zhanbing(College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong, 266590, China)
出处
《山东科技大学学报（自然科学版）》
CAS
北大核心
2021年第3期89-95,共7页
Journal of Shandong University of Science and Technology(Natural Science)
基金
国家自然科学基金项目(11571207)
山东科技大学研究生创新项目(SDKDYC170343)。
关键词
梁方程
LAPLACE变换
不动点定理
正解
迭代方法
beam equations
Laplace transform
fixed point theorem
positive solution
iterative method
