基于方向导数的非线性资产投资模型及其解的性质  

A Nonlinear Asset Investment Model Based on Directional Derivatives and the Properties of Its Solutions

作　　者：张隆[1] 孔凡亮[1] 邢喜民 徐加波[1] ZHANG Long;KONG Fan-liang;XING Xi-min;XU Jia-bo(School of Mathematics and Physics,Xinjiang Institute of Engineering,Urumqi 830023,China)

机构地区：[1]新疆工程学院数理学院,新疆鲁木齐830023

出　　处：《数学的实践与认识》2022年第11期189-196,共8页Mathematics in Practice and Theory

基　　金：新疆维吾尔自治区自然科学基金(2021D01B35、2021D01A65)。

摘　　要：研究了带有柯布道格拉斯生产函数边界条件的非线性资产投资系统的定解问题,通过将依赖资产总量的非线性问题转化为一个算子的不动点的存在唯一性问题,利用Banach空间不动点原理得到了方程解的存在唯一性,讨论了模型解关于外资项的连续依赖性及解的性质.The definite solution problem of nonlinear asset investment system with the boundary condition of neutral production function is studied.The nonlinear problem dependent on the total amount of assets is transformed into the existence and uniqueness problem of the fixed point of an operator.The existence and uniqueness of solutions are obtained by using the fixed point principle of Banach.Finally,the continuous dependence of the model solution on foreign capital terms is discussed.

关 键 词：方向导数 生产函数 积分方程 

分 类 号：O175[理学—数学] F224[理学—基础数学]