含导数项的奇异二阶周期边值问题的正解

Positive Solutions to a Second-Order Singular Periodic Boundary Value Problem with Derivative Argument

在二阶非线性微分方程周期边值问题的基础上,利用锥映射不动点定理,讨论了带有导数项的二阶非线性周期边值问题的正解的存在性,并且允许非线性项具有奇异性这一限制条件,最后给出了解的存在性定理,还把这一结果应用于一个具体的二阶边值问题中,同时对前人的结果进行了改进和推广.

On the basis of nonlinear second-order periodic boundary value problem, the paper mainly discusses the existence of positive solutions to a class of nonlinear second-order singular periodic boundary value problem with derivative argument by using Krasnoselskii fixed point theorem of cone map. The sufficient conditions for positive periodic solutions are obtained. The results are applied to a detailed example, and the traditional results are improved.