%0 Journal Article
%T 一类带非线性边界条件的二阶差分方程正解的多解性<br>Multiplicity of Positive Solutions for a Class of Second-Order Difference Equation with Nonlinear Boundary Conditions
%A 景证棋
%A 路艳琼
%J Advances in Applied Mathematics
%P 4129-4141
%@ 2324-8009
%D 2022
%I Hans Publishing
%R 10.12677/AAM.2022.117440
%X 带非线性边界条件的差分方程边值问题在采用聚氨醋水泥钢丝绳加固桥梁以及求解环形域上椭圆 型方程组正径向解等方面有着重要的应用。本文运用不动点指数定理和上下解方法，当非线性项为正函数且在无穷远处超线性增长时，对充分小的参数，建立了上述问题正解的存在性及多解性的结果，这为微分方程边值问题的数值解提供了理论方法。 最后通过一个例子说明定理结论的有效性。<br />
Boundary value problems of difference equations with nonlinear boundary conditions have many important applications such as in strengthening Bridges with polyurethane cement wire ropes and solving positive radial solutions of elliptic equations in annular domain. In this paper, by using the fixed point index theorem and the method of upper and lower solutions, we obtain the existence and multiplicity of positive solutions to the above problems for sufficiently small parameters when the nonlinear term is a positive function and superlinear growth at infinity. The results provide a theoretical method for numerical solution of boundary value problems of differential equations. Finally, we give an example to illustrate the validity of the main results.
%K 多解性，正解，上下解方法，拓扑度理论<br>Multiplicity
%K Positive Solution
%K Upper and Lower Solutions
%K Topological Degree Theory
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=53270