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-  2018 

一类非线性二阶常微分方程 Dirichlet问题正解的存在性
Existence of positive solutions for a class of nonlinear second-order Dirichlet problem

DOI: 10.6040/j.issn.1671-9352.0.2017.178

Keywords: Green 函数,正解,Dirichlet 问题,存在性,
Green function
,existence,positive solutions,Dirichlet problem

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Abstract:

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。
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

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