一类二阶差分方程边值问题的正解  

Positive Solutions of Boundary Value Problems to a Class of Second Order Difference Equations

作　　者：张政 柏仕坤 彭皓 ZHANG Zheng;BAI Shikun;PENG Hao(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《宿州学院学报》2021年第3期25-27,46,共4页Journal of Suzhou University

基　　金：重庆市自然科学基金面上项目(cstc2020jcyj-msxmX0123);重庆市教委科技项目(KJQN201900539,KJQN202000528)。

摘　　要：研究了一类二阶差分边值问题,将该问题转化为等价的算子方程,构建连续空间上的正锥,结合算子方程格林函数性质,运用不动点指数理论建立了在相关算子第一特征值条件下,非线性项在无穷远处和零点处具有超线性和次线性增长的差分方程边值问题正解的存在性,该条件是研究这类问题的最优条件,推广和改进了近期这方面的一些研究成果。Boundary value problems of a class of second order difference equations are studied and the problems are transformed into an equivalent operator equation.A positive cone in continuous space is constructed.Combined with the properties of Green′s function of operator equations,the existence of positive solutions for the boundary value problem of difference equation with superlinear and sublinear growths of the nonlinear term at infinity and zero is established by using the fixed point index theory under the first eigenvalue condition of the correlation operator which is the optimum condition to study this kind of problem,and it generalizes and improves some recent research results.

关 键 词：二阶差分方程 边值问题 正解 不动点指数 

分 类 号：O175.7[理学—数学]