二阶非线性q-差分微分方程两点边值问题两个迭代正解的存在性

Existence of Two Positive Solutions for Two-Point Boundary Value Problems of Nonlinear Second-Order q-Difference Differential Equations by the Monotonic Iteration Method

研究了二阶非线性q-差分微分方程两点边值问题,给出了系统两个正解存在的充分条件.与其他文献中使用的不动点定理不同,文章不仅证明了该系统正解的存在性,而且还利用单调迭代技巧给出了逼近正解的迭代格式.

The nonlinear second-order q-difference differential equations with two-point boundary value problems are proposed in this paper.Sufficient conditions are given for the existence of two positive solutions of the system.Different from the fixed point theorem used in any other literatures,not only the existence of positive solutions for the system is obtained,but also iterative schemes are constructed for approximating the positive solutions by applying monotone iterative technique in this paper.