%0 Journal Article
%T 一类非线性二阶常微分方程 Dirichlet问题正解的存在性<br>Existence of positive solutions for a class of nonlinear second-order Dirichlet problem
%A 王娇
%J 山东大学学报（理学版）
%D 2018
%R 10.6040/j.issn.1671-9352.0.2017.178
%X 摘要： 运用锥上的不动点定理研究了一类带 Dirichlet 边界条件的二阶边值问题{u″(t)+a(t)u(t)+f(t,u(t))=0, t∈(0,1),u(0)=u(1)=0正解的存在性, 其中 a∈C(［0,1］, ［0,∞))且在(0,1)的任意子区间内 a(t)？0, f∈C(［0,1］×［0,∞), ［0,∞))。所得结果推广和改进了已有工作的相关结果。<br>Abstract: The existence of positive solutions for a class of second-order Dirichlet problem{u″(t)+a(t)u(t)+f(t,u(t))=0, t∈(0,1),u(0)=u(1)=0is studied by using the fixed-point theorem in cones, where a∈C(［0,1］, ［0,∞))and a(t)？0 on any subinterval of(0,1), f∈C(［0,1］×［0,∞), ［0,∞)). The results generalize and improve the related results of the existingwork
%K Green 函数
%K 正解
%K Dirichlet 问题
%K 存在性
%K &lt
%K br&gt
%K Green function
%K existence
%K positive solutions
%K Dirichlet problem
%U http://lxbwk.njournal.sdu.edu.cn/CN/10.6040/j.issn.1671-9352.0.2017.178