摘要
通过构造Green函数,借助锥不动点定理讨论二阶常微分方程两点边值问题u″+u+f(t,u)=0,αu(0)-βu′(0)=0,γu(1)+δu′(1)=0正解的存在性。
This paper study the existence of positive solutions of the differential equation u″+F(t,u)=0 with linear boundary conditions. The existence of at least one positive solution was shown if F is neither superlinear nor sublinear by a simple application of a Fixed Point Theorem in cones. In this paper, the second-order boundary value problem(BVP) was considered. u″+F(t,u)=0, 0<t<1,(1.1) αu(0)-βu′(0)=0, γu(1)+δu′(1)=0(1.2) The following conditions will be assumed throught: (a) F∈C([0,1]×[0,∞)), (b) α,β,γ,δ≥0 (c) 0≤arcsin(βα~2+β~2)≤π2-1, 0≤arcsin(δγ~2+δ~2)≤π2-1. The BVP (1.1),(1.2) arises in many different areas of applied mathematics and physics. Additional existence results may be found in lienture^([2-6]).Our purpose here is to give an existence result for positive solutions to the BVP(1.1),(1.2)assuming that F is neither superlinear nor sublinear.
出处
《河北省科学院学报》
CAS
2004年第4期6-12,共7页
Journal of The Hebei Academy of Sciences
关键词
GREEN函数
锥不动点定理
存在性
Green′s function
Fixed Point Theorem in cones
The existence
